Special Issue "Recent Advances in Fixed Point and Best Proximity Point Problems and Their Applications"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 December 2019

Special Issue Editors

Guest Editor
Prof. Chi-Ming Chen

Institute of Computational and Modeling Science, National Tsing Hua University, 521 Nan-Dah Road, Hsinchu City 30014, Taiwan
Website | E-Mail
Interests: mathematical analysis; functional analysis; fixed point theory
Guest Editor
Prof. Ing-Jer Lin

Department of Mathematics, National Kaohsiung Normal University, 82444 No.62, Shenjhong Road, Yanchao District, Kaohsiung City 82446, Taiwan
Website | E-Mail
Interests: multivariate analysis; harmonic analysis; functional analysis; nonlinear analysis; fixed point theory; mathematics education

Special Issue Information

Dear Colleagues,

The main goal of this Special Issue is to gather the recent results and discussion around reseach in nonlinear (functional) analysis, with a particular interest in the improvements to the theoretical side of fixed point theory that may play a crucial role in the solution of real-world problems.

The fixed point $f(x) = x$ equation is equivalent to F(x) = 0 where F(x) = x − f(x). Thus, the concrete solution of such equations takes "fixed point theory" into account. In cases where it is not possible to solve such a problem, any approximative solution is also worth considering and can be identified through the best proximity point theory. Roughly speaking, best proximity means the minimal value of d(x,f(x)) if f(x) is not equal to x.

These approaches help us to overcome the difficulties arising in the study and computational simulation of nonlinear analysis. For the solution of the problems and/or to identify better solutions, researcher refine the existing axioms and requirements. In this Special Issue, we aim to explore the trends in the solutions of real-world problem, in particular by using the fixed/best-proximity point theory.

Topics for this mini symposium include, but are not limited to:

  • Fixed point of continuous and discontinuous mapping;
  • Existence and uniqueness of the solution of the equation F(x) = 0 = x − f(x);
  • Characterization of completeness for abstract spaces;
  • Iterative methods for the nonexpansive-type mappings;
  • Examination of different types of contractions.

Prof. Chi-Ming Chen
Prof. Ing-Jer Lin
Guest Editors

Manuscript Submission Information

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Keywords

  • Fixed point of single and multivalued mappings
  • Best proximity point of single and multivalued mappings
  • Distinct contractions
  • Applications of fixed point results

Published Papers (8 papers)

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Research

Open AccessArticle
On (G,G)-Prešić–Ćirić Operators in Graphical Metric Spaces
Mathematics 2019, 7(5), 445; https://doi.org/10.3390/math7050445
Received: 15 April 2019 / Revised: 13 May 2019 / Accepted: 13 May 2019 / Published: 18 May 2019
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Abstract
The purpose of this paper is to introduce a new type of operators in graphical metric spaces and to prove some fixed point results for these operators. Several known results are generalized and extended in this new setting of graphical metric spaces. The [...] Read more.
The purpose of this paper is to introduce a new type of operators in graphical metric spaces and to prove some fixed point results for these operators. Several known results are generalized and extended in this new setting of graphical metric spaces. The results are illustrated and justified with examples. Full article
Open AccessArticle
Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces
Mathematics 2019, 7(4), 349; https://doi.org/10.3390/math7040349
Received: 3 April 2019 / Revised: 10 April 2019 / Accepted: 11 April 2019 / Published: 14 April 2019
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Abstract
In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ-contraction via the MT-function. We express some examples to [...] Read more.
In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ -contraction via the MT -function. We express some examples to indicate the validity of the presented results. Our results unify and generalize a number of best proximity point results on the topic in the corresponding recent literature. Full article
Open AccessArticle
Some Remarks and New Results in Ordered Partial b-Metric Spaces
Mathematics 2019, 7(4), 334; https://doi.org/10.3390/math7040334
Received: 17 March 2019 / Revised: 31 March 2019 / Accepted: 3 April 2019 / Published: 6 April 2019
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Abstract
We improve and generalize some new results in fixed point theory in the context of partial b-metric spaces. Full article
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
Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems
Mathematics 2019, 7(2), 123; https://doi.org/10.3390/math7020123
Received: 17 December 2018 / Revised: 18 January 2019 / Accepted: 21 January 2019 / Published: 24 January 2019
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Abstract
The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of [...] Read more.
The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions. Full article
Open AccessArticle
Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance
Mathematics 2019, 7(1), 84; https://doi.org/10.3390/math7010084
Received: 29 November 2018 / Revised: 10 January 2019 / Accepted: 14 January 2019 / Published: 15 January 2019
Cited by 1 | PDF Full-text (231 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we initiate the concept of interpolative Ćirić-Reich-Rus type contractions via the Branciari distance and prove some related fixed points results for such mappings. Moreover, an example is provided to show the useability of our obtained results. Full article
Open AccessArticle
Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions
Mathematics 2019, 7(1), 46; https://doi.org/10.3390/math7010046
Received: 19 November 2018 / Revised: 28 December 2018 / Accepted: 28 December 2018 / Published: 4 January 2019
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Abstract
The purpose of this article is to resolve a global optimization problem for quasi-noncyclic relatively nonexpansive mappings by giving an algorithm that determines an optimal approximate solution of the following minimization problem, minxAd(x,Tx) [...] Read more.
The purpose of this article is to resolve a global optimization problem for quasi-noncyclic relatively nonexpansive mappings by giving an algorithm that determines an optimal approximate solution of the following minimization problem, min x A d ( x , T x ) , min y B d ( y , T y ) and min ( x , y ) A × B d ( x , y ) ; also, we provide some illustrative examples to support our results. As an application, the existence of a solution of the analytic complex function is discussed. Full article
Open AccessArticle
Double Controlled Metric Type Spaces and Some Fixed Point Results
Mathematics 2018, 6(12), 320; https://doi.org/10.3390/math6120320
Received: 12 November 2018 / Revised: 2 December 2018 / Accepted: 7 December 2018 / Published: 12 December 2018
Cited by 3 | PDF Full-text (269 KB) | HTML Full-text | XML Full-text
Abstract
In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α(x,y) and μ(x,y) on the right-hand side of the b-triangle [...] Read more.
In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α ( x , y ) and μ ( x , y ) on the right-hand side of the b - triangle inequality, that is, d ( x , y ) α ( x , z ) d ( x , z ) + μ ( z , y ) d ( z , y ) , for all x , y , z X . Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and ϕ -nonlinear type contractions in the setting of double controlled metric type spaces. Full article
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