Special Issue "Applications in Theoretical and Computational Fixed Point Problems"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (30 November 2019).

Special Issue Editors

Dr. Manuel De la Sen
Website
Guest Editor
University of the Basque Country, Spain
Interests: discrete and sampled-data control systems; nonperiodic and adaptive sampling; adaptive control; fixed point theory; positive systems; stability; models for ecology; epidemic models; time-delay systems; artificial intelligence and heuristic tools for dynamic systems; ordinary differential equations
Special Issues and Collections in MDPI journals
Dr. Hassen Aydi
Website
Guest Editor
Imam Abdulrahman Bin Faisal, University, Department of Mathematics, College of Education of Jubail, P.O. 12020, Industrial Jubail 31961, Saudi Arabia
Interests: Fixed Point Theory and its Applications; Functional Analysis; Operator theory

Special Issue Information

Dear Colleagues,

The origin of the fixed-point theory can be traced back to the middle of the 1980s, to the method of successive approximation for the solutions of certain differential equations. Indeed, fixed point theory lies at the intersection of functional analysis, topology, and applied mathematics. Due to its nature, fixed point theory has a wide application not only in mathematics but also in several qualitative sciences, such as economics, computer sciences, physics, engineering, and so on.

This Special Issue aims to collect significant contributions and advances in theoretical fixed point theory, as well as new and interesting applications in mathematics or other qualitative sciences.

We invite researchers to submit their significant results to this Special Issue with original, high-level papers. Potential topics include but are not limited to the following:

  • Metric fixed-point theorems;
  • Ulam–Hyers stability and well-posedness of fixed-point problems;
  • The computation of fixed points and applications;
  • Approximate solutions of fixed-point problems and applications;
  • Optimization and applications;
  • Ekeland variational principle with applications to fixed point theory;
  • Fractional (integral-differential) calculus;
  • Fixed points of multi-valued monotone operators and the solvability of a fractional integral inclusion;
  • Best proximity theory and its applications;
  • Iterative fixed-point theory;
  • Discrete fixed-point theory

Dr. Hassen Aydi
Dr. Manuel De la Sen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (13 papers)

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Research

Open AccessFeature PaperArticle
Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point
Mathematics 2019, 7(12), 1160; https://doi.org/10.3390/math7121160 - 02 Dec 2019
Cited by 1
Abstract
An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by [...] Read more.
An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by ω . Some test problems are included to verify the accuracy of the proposed methods. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
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Open AccessArticle
Extended Rectangular M-Metric Spaces and Fixed Point Results
Mathematics 2019, 7(12), 1136; https://doi.org/10.3390/math7121136 - 21 Nov 2019
Abstract
In this paper, we enlarge the classes of rectangular M b -metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular M r ξ -metric spaces and utilize the same to prove an analogue of Banach contraction principle [...] Read more.
In this paper, we enlarge the classes of rectangular M b -metric spaces and extended rectangular b-metric spaces by considering the class of extended rectangular M r ξ -metric spaces and utilize the same to prove an analogue of Banach contraction principle in such spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of solution for a system of Fredholm integral equation. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
A New Fixed Point Theorem and a New Generalized Hyers-Ulam-Rassias Stability in Incomplete Normed Spaces
Mathematics 2019, 7(11), 1117; https://doi.org/10.3390/math7111117 - 16 Nov 2019
Abstract
In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous [...] Read more.
In this study, our goal is to apply a new fixed point method to prove the Hyers-Ulam-Rassias stability of a quadratic functional equation in normed spaces which are not necessarily Banach spaces. The results of the present paper improve and extend some previous results. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessFeature PaperArticle
On Common Fixed Point Results for New Contractions with Applications to Graph and Integral Equations
Mathematics 2019, 7(11), 1082; https://doi.org/10.3390/math7111082 - 09 Nov 2019
Abstract
The investigation of symmetric/asymmetric structures and their applications in mathematics (in particular in operator theory and functional analysis) is useful and fruitful. A metric space has the property of symmetry. By looking in the same direction and using the α -admissibility with regard [...] Read more.
The investigation of symmetric/asymmetric structures and their applications in mathematics (in particular in operator theory and functional analysis) is useful and fruitful. A metric space has the property of symmetry. By looking in the same direction and using the α -admissibility with regard to η and θ -functions, we demonstrate some existence and uniqueness fixed point theorems. The obtained results extend and generalize the main result of Isik et al. (2019). At the end, some illustrated applications are presented. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
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Open AccessArticle
A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations
Mathematics 2019, 7(7), 634; https://doi.org/10.3390/math7070634 - 17 Jul 2019
Cited by 2
Abstract
In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and [...] Read more.
In this paper, we obtain coupled fixed point results for F-contraction mapping satisfying a nonlinear contraction condition in the framework of complete metric space without and with a directed graph. As applications of our results, we study a problem of existence and uniqueness of solutions for a class of systems of functional equations that appears in dynamic programming and nonlinear integral equations. Finally, illustrative examples to support some our results are discussed. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Generalized (σ,ξ)-Contractions and Related Fixed Point Results in a P.M.S
Mathematics 2019, 7(5), 481; https://doi.org/10.3390/math7050481 - 27 May 2019
Abstract
In this paper, we present the concept of Θ ( σ , ξ ) Ω -contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and [...] Read more.
In this paper, we present the concept of Θ ( σ , ξ ) Ω -contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and an application are given in order to validate our results. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b-Metric Spaces
Mathematics 2019, 7(5), 478; https://doi.org/10.3390/math7050478 - 26 May 2019
Cited by 3
Abstract
In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler’s fixed point theorem. We also establish some [...] Read more.
In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler’s fixed point theorem. We also establish some fixed point results, which generalize our first result. Furthermore, we establish Mizoguchi–Takahashi’s type fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U that improves many existing results in the literature. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Picard-Jungck Operator for a Pair of Mappings and Simulation Type Functions
Mathematics 2019, 7(5), 461; https://doi.org/10.3390/math7050461 - 22 May 2019
Cited by 1
Abstract
In this manuscript, we propose a new class of Picard-Jungck operators for a pair of mappings on complete metric spaces by taking into account of the C G -simulation function. Also, some new results for the existence of such operators for a pair [...] Read more.
In this manuscript, we propose a new class of Picard-Jungck operators for a pair of mappings on complete metric spaces by taking into account of the C G -simulation function. Also, some new results for the existence of such operators for a pair of self mappings in the setting of metric spaces are obtained. Some nontrivial examples are presented to show the usability of the results. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations
Mathematics 2019, 7(5), 444; https://doi.org/10.3390/math7050444 - 18 May 2019
Cited by 3
Abstract
In this manuscript, we introduce a new notion: a Berinde type ( α , ψ ) -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. [...] Read more.
In this manuscript, we introduce a new notion: a Berinde type ( α , ψ ) -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Common Fixed Point Results for Rational (α,β)φ- Contractions in Complete Quasi Metric Spaces
Mathematics 2019, 7(5), 392; https://doi.org/10.3390/math7050392 - 30 Apr 2019
Cited by 4
Abstract
The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational [...] Read more.
The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational ( α , β ) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Weak Partial b-Metric Spaces and Nadler’s Theorem
Mathematics 2019, 7(4), 332; https://doi.org/10.3390/math7040332 - 05 Apr 2019
Cited by 1
Abstract
The purpose of this paper is to define the notions of weak partial b-metric spaces and weak partial Hausdorff b-metric spaces along with the topology of weak partial b-metric space. Moreover, we present a generalization of Nadler’s theorem by using [...] Read more.
The purpose of this paper is to define the notions of weak partial b-metric spaces and weak partial Hausdorff b-metric spaces along with the topology of weak partial b-metric space. Moreover, we present a generalization of Nadler’s theorem by using weak partial Hausdorff b-metric spaces in the context of a weak partial b-metric space. We present a non-trivial example which show the validity of our result and an application to nonlinear Volterra integral inclusion for the applicability purpose. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces
Mathematics 2019, 7(4), 327; https://doi.org/10.3390/math7040327 - 03 Apr 2019
Cited by 1
Abstract
The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable [...] Read more.
The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained herein. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
Open AccessArticle
Fixed Point Results for α*-ψ-Dominated Multivalued Contractive Mappings Endowed with Graphic Structure
Mathematics 2019, 7(3), 307; https://doi.org/10.3390/math7030307 - 26 Mar 2019
Cited by 2
Abstract
The purpose of this paper is to establish fixed point results for a pair α -dominated multivalued mappings fulfilling generalized locally new α - ψ -Ćirić type rational contractive conditions on a closed ball in complete dislocated metric spaces. Examples and [...] Read more.
The purpose of this paper is to establish fixed point results for a pair α -dominated multivalued mappings fulfilling generalized locally new α - ψ -Ćirić type rational contractive conditions on a closed ball in complete dislocated metric spaces. Examples and applications are given to demonstrate the novelty of our results. Our results extend several comparable results in the existing literature. Full article
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
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