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Mathematics, Volume 7, Issue 2 (February 2019)

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Cover Story (view full-size image) Derivatives and integrals of arbitrary non-integer (fractional) order were introduced by Leibniz, [...] Read more.
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Open AccessArticle A Classification of Symmetric (1, 1)-Coherent Pairs of Linear Functionals
Mathematics 2019, 7(2), 213; https://doi.org/10.3390/math7020213
Received: 27 November 2018 / Revised: 13 February 2019 / Accepted: 15 February 2019 / Published: 25 February 2019
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Abstract
In this paper, we study a classification of symmetric ( 1 , 1 ) -coherent pairs by using a symmetrization process. In particular, the positive-definite case is carefully described. Full article
Open AccessFeature PaperArticle On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights
Mathematics 2019, 7(2), 212; https://doi.org/10.3390/math7020212
Received: 16 January 2019 / Revised: 7 February 2019 / Accepted: 8 February 2019 / Published: 25 February 2019
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Abstract
Let 1<a<b<c<d and α^5:=1,a,b,c,d be a weighted sequence that is recursively generated by five weights 1,a,b, [...] Read more.
Let 1 < a < b < c < d and α ^ 5 : = 1 , a , b , c , d be a weighted sequence that is recursively generated by five weights 1 , a , b , c , d . In this paper, we give sufficient conditions for the positive quadratic hyponormalities of W α x and W α y , x , with α x : x , α ^ 5 and α y , x : y , x , α ^ 5 . Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications)
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Open AccessArticle Stability Analysis of Singly Diagonally Implicit Block Backward Differentiation Formulas for Stiff Ordinary Differential Equations
Mathematics 2019, 7(2), 211; https://doi.org/10.3390/math7020211
Received: 14 November 2018 / Revised: 27 January 2019 / Accepted: 28 January 2019 / Published: 25 February 2019
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Abstract
In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal diagonal elements which will results in only one evaluation [...] Read more.
In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal diagonal elements which will results in only one evaluation of the Jacobian and one LU decomposition for each time step. For the SDIBBDF method to have practical significance in solving stiff problems, its stability region must at least cover almost the whole of the negative half plane. Step size restriction of the proposed method have to be considered in order to ensure stability of the method in computing numerical results. Efficiency of the SDIBBDF method in solving stiff ODEs is justified when it managed to outperform the existing methods for both accuracy and computational time. Full article
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Open AccessArticle More Results on the Domination Number of Cartesian Product of Two Directed Cycles
Mathematics 2019, 7(2), 210; https://doi.org/10.3390/math7020210
Received: 12 December 2018 / Revised: 12 February 2019 / Accepted: 21 February 2019 / Published: 24 February 2019
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Abstract
Let γ(D) denote the domination number of a digraph D and let CmCn denote the Cartesian product of Cm and Cn, the directed cycles of length nm3. Liu [...] Read more.
Let γ ( D ) denote the domination number of a digraph D and let C m C n denote the Cartesian product of C m and C n , the directed cycles of length n m 3 . Liu et al. obtained the exact values of γ ( C m C n ) for m up to 6 [Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36–39]. Shao et al. determined the exact values of γ ( C m C n ) for m = 6 , 7 [On the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 619695]. Mollard obtained the exact values of γ ( C m C n ) for m = 3 k + 2 [M. Mollard, On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths, Discuss. Math. Graph Theory 33(2) (2013) 387–394.]. In this paper, we extend the current known results on C m C n with m up to 21. Moreover, the exact values of γ ( C n C n ) with n up to 31 are determined. Full article
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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Open AccessArticle Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)
Mathematics 2019, 7(2), 209; https://doi.org/10.3390/math7020209
Received: 26 January 2019 / Revised: 13 February 2019 / Accepted: 14 February 2019 / Published: 24 February 2019
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Abstract
This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order α(1,2). The main tools of our study include the [...] Read more.
This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order α ( 1 , 2 ) . The main tools of our study include the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed-point theorem. As an application, we apply the obtained results to a control problem. Full article
Open AccessArticle Evaluation of the Impact of Strategic Offers on the Financial and Strategic Health of the Company—A Soft System Dynamics Approach
Mathematics 2019, 7(2), 208; https://doi.org/10.3390/math7020208
Received: 29 December 2018 / Revised: 14 February 2019 / Accepted: 19 February 2019 / Published: 24 February 2019
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Abstract
When analyzing the possibility of supporting the decision-making process, one should take into account the essential properties of economic entities (the system and its objects). As a result, the development of an effective business model ought to be based on rationality and the [...] Read more.
When analyzing the possibility of supporting the decision-making process, one should take into account the essential properties of economic entities (the system and its objects). As a result, the development of an effective business model ought to be based on rationality and the characteristics of the system being modeled. Such an approach implies the use of an appropriate analysis and modeling method. Since the majority of relationships in the model are described using the experts’ tacit knowledge, methods known as “soft” are more suitable than “hard” in those situations. Fuzzy cognitive mappings (FCM) are therefore commonly used as a technique for participatory modeling of the system, where stakeholders can convey their knowledge to the model of the system in question. In this study, we introduce a novel approach: the extended weighted influence nonlinear gauge system (WINGS), which may equally well be applied to the decision problems of this type. Appraisal of high-value and long-term offers in the sector of the telecommunication supplier industry serves as a real-world case study for testing the new method. A comparison with FCM provides a deeper understanding of the similarities and differences of the two approaches. Full article
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
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Open AccessArticle Extended Local Convergence for the Combined Newton-Kurchatov Method Under the Generalized Lipschitz Conditions
Mathematics 2019, 7(2), 207; https://doi.org/10.3390/math7020207
Received: 4 February 2019 / Revised: 19 February 2019 / Accepted: 20 February 2019 / Published: 23 February 2019
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Abstract
We present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipschitz-type condition and the notion of the restricted convergence [...] Read more.
We present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipschitz-type condition and the notion of the restricted convergence region. These modifications of earlier conditions result in a tighter convergence analysis and more precise information on the location of the solution. These advantages are obtained under the same computational effort. Using illuminating examples, we further justify the superiority of our new results over earlier ones. Full article
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
Open AccessArticle Generalized Fractional Integral Operators Pertaining to the Product of Srivastava’s Polynomials and Generalized Mathieu Series
Mathematics 2019, 7(2), 206; https://doi.org/10.3390/math7020206
Received: 31 December 2018 / Revised: 16 February 2019 / Accepted: 20 February 2019 / Published: 23 February 2019
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Abstract
Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the [...] Read more.
Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral operators involving hypergeometric function in the kernel are applied to the product of Srivastava’s polynomials and the generalized Mathieu series, containing the factor x λ ( x k + c k ) ρ in its argument. The results are expressed in terms of the generalized hypergeometric function and Hadamard product of the generalized Mathieu series. Corresponding special cases related to the Riemann–Liouville and Erdélyi–Kober fractional integral operators are also considered. Full article
(This article belongs to the Special Issue Special Functions and Applications)
Open AccessArticle Dini-Type Helicoidal Hypersurfaces with Timelike Axis in Minkowski 4-Space E14
Mathematics 2019, 7(2), 205; https://doi.org/10.3390/math7020205
Received: 31 January 2019 / Revised: 11 February 2019 / Accepted: 13 February 2019 / Published: 22 February 2019
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Abstract
We consider Ulisse Dini-type helicoidal hypersurfaces with timelike axis in Minkowski 4-space E14. Calculating the Gaussian and the mean curvatures of the hypersurfaces, we demonstrate some special symmetries for the curvatures when they are flat and minimal. [...] Read more.
We consider Ulisse Dini-type helicoidal hypersurfaces with timelike axis in Minkowski 4-space E 1 4 . Calculating the Gaussian and the mean curvatures of the hypersurfaces, we demonstrate some special symmetries for the curvatures when they are flat and minimal. Full article
(This article belongs to the Special Issue Computer Algebra in Scientific Computing)
Open AccessArticle On the Domain of the Fibonacci Difference Matrix
Mathematics 2019, 7(2), 204; https://doi.org/10.3390/math7020204
Received: 31 December 2018 / Revised: 17 February 2019 / Accepted: 19 February 2019 / Published: 21 February 2019
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Abstract
Matrix F^ derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces lp(F) and l(F); (1 ≤ p < ∞) were examined. Then, Başarır et al. (2015) defined the spaces c [...] Read more.
Matrix F^ derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces lp(F) and l(F); (1 ≤ p < ∞) were examined. Then, Başarır et al. (2015) defined the spaces c0(F) and c(F) and Candan (2015) examined the spaces c(F(r,s)) and c0(F(r,s)). Later, Yaşar and Kayaduman (2018) defined and studied the spaces cs(F(s,r)) and bs(F(s,r)). In this study, we built the spaces cs(F) and bs(F). They are the domain of the matrix F on cs and bs, where F is a triangular matrix defined by Fibonacci Numbers. Some topological and algebraic properties, isomorphism, inclusion relations and norms, which are defined over them are examined. It is proven that cs(F) and bs(F) are Banach spaces. It is determined that they have the γ, β, α -duals. In addition, the Schauder base of the space cs(F) are calculated. Finally, a number of matrix transformations of these spaces are found. Full article
Open AccessArticle k-Rainbow Domination Number of P3Pn
Mathematics 2019, 7(2), 203; https://doi.org/10.3390/math7020203
Received: 12 January 2019 / Revised: 5 February 2019 / Accepted: 19 February 2019 / Published: 21 February 2019
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Abstract
Let k be a positive integer, and set [k]:={1,2,,k}. For a graph G, a k-rainbow dominating function (or kRDF) of G is a mapping f:V [...] Read more.
Let k be a positive integer, and set [ k ] : = { 1 , 2 , , k } . For a graph G, a k-rainbow dominating function (or kRDF) of G is a mapping f : V ( G ) 2 [ k ] in such a way that, for any vertex v V ( G ) with the empty set under f, the condition u N G ( v ) f ( u ) = [ k ] always holds, where N G ( v ) is the open neighborhood of v. The weight of kRDF f of G is the summation of values of all vertices under f. The k-rainbow domination number of G, denoted by γ r k ( G ) , is the minimum weight of a kRDF of G. In this paper, we obtain the k-rainbow domination number of grid P 3 P n for k { 2 , 3 , 4 } . Full article
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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Open AccessArticle Stanley Depth of Edge Ideals of Some Wheel-Related Graphs
Mathematics 2019, 7(2), 202; https://doi.org/10.3390/math7020202
Received: 28 December 2018 / Revised: 4 February 2019 / Accepted: 6 February 2019 / Published: 21 February 2019
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Abstract
Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In particular, we establish [...] Read more.
Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In particular, we establish general closed formulas for Stanley depth of quotient of edge ideals associated with the m t h -power of a wheel graph, for m 3 , gear graphs and anti-web gear graphs. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
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Open AccessArticle Further Results on the Resistance-Harary Index of Unicyclic Graphs
Mathematics 2019, 7(2), 201; https://doi.org/10.3390/math7020201
Received: 20 December 2018 / Revised: 14 February 2019 / Accepted: 14 February 2019 / Published: 20 February 2019
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Abstract
The Resistance-Harary index of a connected graph G is defined as RH(G)={u,v}V(G)1r(u,v), where r(u,v) [...] Read more.
The Resistance-Harary index of a connected graph G is defined as R H ( G ) = { u , v } V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G. A graph G is called a unicyclic graph if it contains exactly one cycle and a fully loaded unicyclic graph is a unicyclic graph that no vertex with degree less than three in its unique cycle. Let U ( n ) and U ( n ) be the set of unicyclic graphs and fully loaded unicyclic graphs of order n, respectively. In this paper, we determine the graphs of U ( n ) with second-largest Resistance-Harary index and determine the graphs of U ( n ) with largest Resistance-Harary index. Full article
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
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Open AccessArticle Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative
Mathematics 2019, 7(2), 200; https://doi.org/10.3390/math7020200
Received: 31 December 2018 / Revised: 13 February 2019 / Accepted: 15 February 2019 / Published: 20 February 2019
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Abstract
In this paper, stability analysis of a fractional-order linear system described by the Caputo–Fabrizio (CF) derivative is studied. In order to solve the problem, character equation of the system is defined at first by using the Laplace transform. Then, some simple necessary and [...] Read more.
In this paper, stability analysis of a fractional-order linear system described by the Caputo–Fabrizio (CF) derivative is studied. In order to solve the problem, character equation of the system is defined at first by using the Laplace transform. Then, some simple necessary and sufficient stability conditions and sufficient stability conditions are given which will be the basis of doing research of a fractional-order system with a CF derivative. In addition, the difference of stability domain between two linear systems described by two different fractional derivatives is also studied. Our results permit researchers to check the stability by judging the locations in the complex plane of the dynamic matrix eigenvalues of the state space. Full article
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Open AccessArticle Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields Q p over Primes p
Mathematics 2019, 7(2), 199; https://doi.org/10.3390/math7020199
Received: 11 December 2018 / Revised: 12 February 2019 / Accepted: 15 February 2019 / Published: 19 February 2019
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Abstract
In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space (LS,τ0) induced by measurable functions on p-adic number fields Qp over primes p. In particular, we are interested in [...] Read more.
In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p . In particular, we are interested in the cases where such free-probabilistic information is affected by primes in given closed intervals of the set R of real numbers by defining suitable “truncated” linear functionals on LS . Full article
(This article belongs to the Special Issue Mathematical Physics II)
Open AccessArticle Convergence Analysis of Weighted-Newton Methods of Optimal Eighth Order in Banach Spaces
Mathematics 2019, 7(2), 198; https://doi.org/10.3390/math7020198
Received: 12 December 2018 / Revised: 14 February 2019 / Accepted: 17 February 2019 / Published: 19 February 2019
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Abstract
We generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study their local convergence. In a previous study, the Taylor expansion of higher order derivatives is employed which may not exist or may be very expensive to compute. However, [...] Read more.
We generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study their local convergence. In a previous study, the Taylor expansion of higher order derivatives is employed which may not exist or may be very expensive to compute. However, the hypotheses of the present study are based on the first Fréchet-derivative only, thereby the application of methods is expanded. New analysis also provides the radius of convergence, error bounds and estimates on the uniqueness of the solution. Such estimates are not provided in the approaches that use Taylor expansions of derivatives of higher order. Moreover, the order of convergence for the methods is verified by using computational order of convergence or approximate computational order of convergence without using higher order derivatives. Numerical examples are provided to verify the theoretical results and to show the good convergence behavior. Full article
(This article belongs to the Special Issue Computational Methods in Analysis and Applications)
Open AccessArticle Sculpture from Patchwise Modules
Mathematics 2019, 7(2), 197; https://doi.org/10.3390/math7020197
Received: 1 December 2018 / Revised: 14 January 2019 / Accepted: 26 January 2019 / Published: 19 February 2019
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Abstract
The sculptor adapts the geometry of spline surfaces commonly used in 3D modeling programs in order to translate some of the topological nature of these virtual surfaces into his sculpture. He realizes the patchwise geometry of such surfaces by gluing square modules of [...] Read more.
The sculptor adapts the geometry of spline surfaces commonly used in 3D modeling programs in order to translate some of the topological nature of these virtual surfaces into his sculpture. He realizes the patchwise geometry of such surfaces by gluing square modules of neoprene rubber edge to edge to define the surface which he then torques and bends into sculptures. While limited by the nature of actual materials, the finished sculptures successfully incorporate the expressive tension and flow of forms sought by the sculptor. He presents images of finished works and provides an analysis of the emotive values of a select sculpture. Full article
(This article belongs to the Special Issue Topological Modeling)
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Open AccessArticle Some Remarks on Harmonic Functions in Minkowski Spaces
Mathematics 2019, 7(2), 196; https://doi.org/10.3390/math7020196
Received: 16 December 2018 / Revised: 15 February 2019 / Accepted: 15 February 2019 / Published: 19 February 2019
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Abstract
We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, [...] Read more.
We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfying the mean value formula must be a harmonic function, then the Minkowski space is Euclidean. Full article
Open AccessArticle Modified Roller Coaster Surface in Space
Mathematics 2019, 7(2), 195; https://doi.org/10.3390/math7020195
Received: 31 December 2018 / Revised: 11 February 2019 / Accepted: 13 February 2019 / Published: 19 February 2019
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Abstract
In this paper, a new modified roller coaster surface according to a modified orthogonal frame is investigated in Euclidean 3-space. In this method, a new modified roller coaster surface is modeled. Both the Gaussian curvature and mean curvature of roller coaster surfaces are [...] Read more.
In this paper, a new modified roller coaster surface according to a modified orthogonal frame is investigated in Euclidean 3-space. In this method, a new modified roller coaster surface is modeled. Both the Gaussian curvature and mean curvature of roller coaster surfaces are investigated. Subsequently, we obtain several characterizations in Euclidean 3-space. Full article
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Open AccessArticle Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application
Mathematics 2019, 7(2), 194; https://doi.org/10.3390/math7020194
Received: 18 January 2019 / Revised: 3 February 2019 / Accepted: 17 February 2019 / Published: 18 February 2019
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Abstract
The purpose of this paper is to introduce the notion of generalized multivalued ψ,ϕ-type contractions and generalized multivalued ψ,ϕ-type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. [...] Read more.
The purpose of this paper is to introduce the notion of generalized multivalued ψ , ϕ-type contractions and generalized multivalued ψ , ϕ-type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. Our results are extension and improvement of the Suzuki and Nadler contraction theorems, Jleli and Samet, Piri and Kumam, Mizoguchi and Takahashi, and Liu et al. fixed point theorems. We provide an example for supporting our new results. Moreover, an application of our main result to the existence of solution of system of functional equations is also presented. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Open AccessArticle Some Common Fixed Point Theorems in Ordered Partial Metric Spaces via ℱ-Generalized Contractive Type Mappings
Mathematics 2019, 7(2), 193; https://doi.org/10.3390/math7020193
Received: 23 December 2018 / Revised: 29 January 2019 / Accepted: 12 February 2019 / Published: 18 February 2019
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Abstract
In the present work, the concept of F-generalized contractive type mappings by using C-class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results [...] Read more.
In the present work, the concept of F -generalized contractive type mappings by using C -class functions is introduced, and some common fixed point results for weakly isotone increasing set-valued mappings in the setting of ordered partial metric spaces are studied. These results improve and generalize various results existing in the literature. The effectiveness of the obtained results is verified with the help of some comparative examples. Full article
(This article belongs to the Special Issue Recent Advances in Fixed Point Theory and Its Applications)
Open AccessArticle Staff Task-Based Shift Scheduling Solution with an ANP and Goal Programming Method in a Natural Gas Combined Cycle Power Plant
Mathematics 2019, 7(2), 192; https://doi.org/10.3390/math7020192
Received: 22 November 2018 / Revised: 30 January 2019 / Accepted: 31 January 2019 / Published: 18 February 2019
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Abstract
Shift scheduling problems (SSPs) are advanced NP-hard problems which are generally evaluated with integer programming. This study presents an applicable shift schedule of workers in a large-scale natural gas combined cycle power plant (NGCCPP), which realize 35.17% of the total electricity generation in [...] Read more.
Shift scheduling problems (SSPs) are advanced NP-hard problems which are generally evaluated with integer programming. This study presents an applicable shift schedule of workers in a large-scale natural gas combined cycle power plant (NGCCPP), which realize 35.17% of the total electricity generation in Turkey alone, as at of the end of 2018. This study included 80 workers who worked three shifts in the selected NGCCPP for 30 days. The proposed scheduling model was solved according to the skills of the workers, and there were nine criteria by which the workers were evaluated for their abilities. Analytic network process (ANP) is a method used for obtaining the weights of workers’ abilities in a particular skill. These weights are used in the proposed scheduling model as concepts in goal programming (GP). The SSP–ANP–GP model sees employees’ everyday preferences as their main feature, bringing high-performance to the highest level, and bringing an objective functionality, and lowering the lowest success of daily choice. At the same time, the model introduced large-scale and soft constraints that reflect the nature of the shift requirements of this program by specifying the most appropriate program. The required data were obtained from the selected NGCCPP and the model solutions were approved by the plant experts. The SSP–ANP–GP model was resolved at a reasonable time. Monthly acquisition time was significantly reduced, and the satisfaction of the employees was significantly increased by using the obtained program. When past studies were examined, it was determined that a shift scheduling problem of this size in the energy sector had not previously been studied. Full article
(This article belongs to the Special Issue Optimization for Decision Making)
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Open AccessArticle Application of Exponential Jensen Picture Fuzzy Divergence Measure in Multi-Criteria Group Decision Making
Mathematics 2019, 7(2), 191; https://doi.org/10.3390/math7020191
Received: 14 January 2019 / Revised: 13 February 2019 / Accepted: 13 February 2019 / Published: 17 February 2019
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Abstract
A divergence measure plays a crucial part in discriminating two probability distributions and drawing inferences constructed on such discrimination. The intention of this study is to propose such a divergence measure based on Jensen inequality and exponential entropy in the settings of probability [...] Read more.
A divergence measure plays a crucial part in discriminating two probability distributions and drawing inferences constructed on such discrimination. The intention of this study is to propose such a divergence measure based on Jensen inequality and exponential entropy in the settings of probability theory. Further, the idea has been generalized to fuzzy sets to familiarize a novel picture fuzzy divergence measure. Besides proposing the validity, some of its key properties are also deliberated. Finally, two illustrative examples are solved based on the proposed picture fuzzy divergence measure which shows the expediency and effectiveness of the proposed approach. Full article
(This article belongs to the Section Mathematics and Computers Science)
Open AccessFeature PaperArticle Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition
Mathematics 2019, 7(2), 190; https://doi.org/10.3390/math7020190
Received: 7 January 2019 / Revised: 13 February 2019 / Accepted: 14 February 2019 / Published: 17 February 2019
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Abstract
In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order α(0,1). Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover, we establish the approximate [...] Read more.
In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order α ( 0 , 1 ) . Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover, we establish the approximate controllability of the problem by applying a unique continuation property via internal control which acts on a sub-domain. Full article
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Open AccessArticle Effects of Preservation Technology Investment on Waste Generation in a Two-Echelon Supply Chain Model
Mathematics 2019, 7(2), 189; https://doi.org/10.3390/math7020189
Received: 27 December 2018 / Revised: 11 February 2019 / Accepted: 13 February 2019 / Published: 17 February 2019
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Abstract
This study develops an integrated production-inventory model for a two-echelon supply chain network with controllable probabilistic deterioration. The investment in preservation technology is considered a decision variable to control the deteriorated quantity of an integrated system. The objective of the study is to [...] Read more.
This study develops an integrated production-inventory model for a two-echelon supply chain network with controllable probabilistic deterioration. The investment in preservation technology is considered a decision variable to control the deteriorated quantity of an integrated system. The objective of the study is to optimize preservation investment, the number of shipments and shipment quantity, so that the total cost per unit of time of the supply chain is minimized. The study proposes a solution method, and the results show that investment in preservation technology reduces the total supply chain cost by 13%. Additionally, preservation increases the lot size, thus increasing the production cycle length, which reduces the ordering cost of the system. Furthermore, this study shows that preservation leads to a reduction of solid waste from deteriorated products. Total deteriorated products reduced to 8 units from 235 units, hence, preservation generates positive environmental benefits along with economic impacts. The robustness of the proposed model is illustrated with a numerical example, sensitivity analysis, and graphical representations. Moreover, comparative study and managerial insights are given to extract significant insights from the model. Full article
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Open AccessFeature PaperArticle Approximation by Sequence of Operators Involving Analytic Functions
Mathematics 2019, 7(2), 188; https://doi.org/10.3390/math7020188
Received: 11 December 2018 / Revised: 11 February 2019 / Accepted: 14 February 2019 / Published: 16 February 2019
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Abstract
In this contribution, we define a new operator sequence which contains analytic functions. Using approximation techniques found by Korovkin, some results are derived. Moreover, a generalization of this operator sequence called Kantorovich type generalization is introduced. Full article
(This article belongs to the Section Mathematics and Computers Science)
Open AccessArticle Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems
Mathematics 2019, 7(2), 187; https://doi.org/10.3390/math7020187
Received: 30 December 2018 / Revised: 2 February 2019 / Accepted: 13 February 2019 / Published: 16 February 2019
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Abstract
In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem [...] Read more.
In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions. Full article
Open AccessArticle The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition
Mathematics 2019, 7(2), 186; https://doi.org/10.3390/math7020186
Received: 19 January 2019 / Revised: 10 February 2019 / Accepted: 14 February 2019 / Published: 16 February 2019
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Abstract
In this article, by using the monotone iterative technique coupled with the method of upper and lower solution, we obtain the existence of extremal iteration solutions to conformable fractional differential equations involving Riemann-Stieltjes integral boundary conditions. At the same time, the comparison principle [...] Read more.
In this article, by using the monotone iterative technique coupled with the method of upper and lower solution, we obtain the existence of extremal iteration solutions to conformable fractional differential equations involving Riemann-Stieltjes integral boundary conditions. At the same time, the comparison principle of solving such problems is investigated. Finally, an example is given to illustrate our main results. It should be noted that the conformal fractional derivative is essentially a modified version of the first-order derivative. Our results show that such known results can be translated and stated in the setting of the so-called conformal fractional derivative. Full article
Open AccessArticle Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity
Mathematics 2019, 7(2), 185; https://doi.org/10.3390/math7020185
Received: 27 December 2018 / Revised: 13 February 2019 / Accepted: 14 February 2019 / Published: 16 February 2019
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Abstract
In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the [...] Read more.
In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
Open AccessArticle A Multi-Objective DV-Hop Localization Algorithm Based on NSGA-II in Internet of Things
Mathematics 2019, 7(2), 184; https://doi.org/10.3390/math7020184
Received: 17 December 2018 / Revised: 6 February 2019 / Accepted: 7 February 2019 / Published: 15 February 2019
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Abstract
Locating node technology, as the most fundamental component of wireless sensor networks (WSNs) and internet of things (IoT), is a pivotal problem. Distance vector-hop technique (DV-Hop) is frequently used for location node estimation in WSN, but it has a poor estimation precision. In [...] Read more.
Locating node technology, as the most fundamental component of wireless sensor networks (WSNs) and internet of things (IoT), is a pivotal problem. Distance vector-hop technique (DV-Hop) is frequently used for location node estimation in WSN, but it has a poor estimation precision. In this paper, a multi-objective DV-Hop localization algorithm based on NSGA-II is designed, called NSGA-II-DV-Hop. In NSGA-II-DV-Hop, a new multi-objective model is constructed, and an enhanced constraint strategy is adopted based on all beacon nodes to enhance the DV-Hop positioning estimation precision, and test four new complex network topologies. Simulation results demonstrate that the precision performance of NSGA-II-DV-Hop significantly outperforms than other algorithms, such as CS-DV-Hop, OCS-LC-DV-Hop, and MODE-DV-Hop algorithms. Full article
(This article belongs to the Special Issue Evolutionary Computation)
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