Special Issue "Nonlinear Problems and Applications of Fixed Point Theory"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 July 2021.

Special Issue Editors

Prof. Dr. Yeol Je Cho
E-Mail Website
Guest Editor
Graduate School, Mathematics, Gyeongsang National University University, Jinju 52828, Korea
Interests: fixed point theory and applications; stability of functional equations; variational inequality problems; equilibrium problems; optimization problems; inequality theory and applications
Special Issues and Collections in MDPI journals
Prof. Dr. Sang-Eon Han
E-Mail Website
Guest Editor
Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju-City, Jeonbuk 54896, Korea
Interests: topology; algebraic topology; digital topology; combinatorial topology; graph theory; discrete mathematics; applied topology; discrete and digital geometry; fixed point theory
Special Issues and Collections in MDPI journals
Prof. Dr. Jong Kyu Kim
E-Mail Website
Guest Editor
Department of Mathematics Education, Kyungnam University, Changwon, Gyeongnam, 51767, Korea
Interests: variational inequality problems; fixed point problems; equilibrium problems; nonlinear analysis; operator equations

Special Issue Information

Dear Colleagues,

Recently, fixed point theory (with topological fixed point theory, metric fixed point theory and discrete fixed point theory) is a very important and powerful tool to study nonlinear analysis and applications, especially, nonlinear operator theory and applications, equilibrium problems and applications, variational inequality problems and applications, complementarity problems and applications, saddle point theory and applications, differential and integral equations and applications, optimization problems and applications, approximation theory and applications, numerical analysis and applications, stability of functional equations, game theory and applications, programming problems and applications, engineering, topology, economics, geometry and many others.

The aim of Special Issue of the journal Mathematics is to enhance the new development of fixed point theory and related nonlinear problems with applications. Our Guest Editors will accept very high quality papers containing original results and survey articles of exceptional merits.

Prof. Dr. Yeol Je Cho
Prof. Dr. Sang-Eon Han
Prof. Dr. Jong Kyu Kim
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 semimonthly 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 1600 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.

Keywords

  • fixed point theory and applications
  • best proximity point theory and applications
  • nonlinear operator theory and applications
  • generalized contractive mappings
  • equilibrium problems and applications
  • variational inequality problems and applications
  • optimization problems and applications
  • game theory and applications
  • numerical algorithms for nonlinear problems
  • well-posedness in fixed point theory
  • stability of functional equations related to fixed point theory
  • differential and integral equations by fixed point theory

Published Papers (8 papers)

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Research

Article
Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations
Mathematics 2021, 9(5), 541; https://doi.org/10.3390/math9050541 - 04 Mar 2021
Viewed by 296
Abstract
The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of [...] Read more.
The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
Article
Discrete Group Actions on Digital Objects and Fixed Point Sets by Isok(·)-Actions
Mathematics 2021, 9(3), 290; https://doi.org/10.3390/math9030290 - 01 Feb 2021
Viewed by 428
Abstract
Given a digital image (or digital object) (X,k),XZn, this paper initially establishes a group structure of the set of self-k-isomorphisms of (X,k) with the function composition, denoted by Isok(X) or Autk(X). In particular, let Ckn,l be a simple closed k-curve with l elements in Zn. Then, the group Isok(Ckn,l) is proved to be isomorphic to the standard dihedral group Dl with order l. The calculation of this quantity Isok(Ckn,l) is a key step for obtaining many new results. Indeed, it is essential for exploring many features of Isok(X). Furthermore, this quantity is proved to be a digital topological invariant. After proceeding with an Isok(X)-action on (X,k), we investigate some properties of fixed point sets by this action. Finally, we explore various features of fixed point sets by this action from the viewpoint of digital k-curve theory. This paper only deals with k-connected digital images (X,k) whose cardinality is equal to or greater than 2. Besides, we discuss some errors that have appeared in the lilterature. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
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Article
Approximation of the Constant in a Markov-Type Inequality on a Simplex Using Meta-Heuristics
Mathematics 2021, 9(3), 264; https://doi.org/10.3390/math9030264 - 29 Jan 2021
Viewed by 355
Abstract
Markov-type inequalities are often used in numerical solutions of differential equations, and their constants improve error bounds. In this paper, the upper approximation of the constant in a Markov-type inequality on a simplex is considered. To determine the constant, the minimal polynomial and [...] Read more.
Markov-type inequalities are often used in numerical solutions of differential equations, and their constants improve error bounds. In this paper, the upper approximation of the constant in a Markov-type inequality on a simplex is considered. To determine the constant, the minimal polynomial and pluripotential theories were employed. They include a complex equilibrium measure that solves the extreme problem by minimizing the energy integral. Consequently, examples of polynomials of the second degree are introduced. Then, a challenging bilevel optimization problem that uses the polynomials for the approximation was formulated. Finally, three popular meta-heuristics were applied to the problem, and their results were investigated. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
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Article
Fixed Point Sets of Digital Curves and Digital Surfaces
Mathematics 2020, 8(11), 1896; https://doi.org/10.3390/math8111896 - 31 Oct 2020
Cited by 1 | Viewed by 442
Abstract
Given a digital image (or digital object) (X,k), we address some unsolved problems related to the study of fixed point sets of k-continuous self-maps of (X,k) from the viewpoints of digital curve and digital surface theory. Consider two simple closed k-curves with li elements in Zn, i{1,2},l1l24. After initially formulating an alignment of fixed point sets of a digital wedge of these curves, we prove that perfectness of it depends on the numbers li,i{1,2}, instead of the k-adjacency. Furthermore, given digital k-surfaces, we also study an alignment of fixed point sets of digital k-surfaces and digital wedges of them. Finally, given a digital image which is not perfect, we explore a certain condition that makes it perfect. In this paper, each digital image (X,k) is assumed to be k-connected and X2 unless stated otherwise. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
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Article
The Most Refined Axiom for a Digital Covering Space and Its Utilities
Mathematics 2020, 8(11), 1868; https://doi.org/10.3390/math8111868 - 27 Oct 2020
Cited by 1 | Viewed by 558
Abstract
This paper is devoted to establishing the most refined axiom for a digital covering space which remains open. The crucial step in making our approach is to simplify the notions of several types of earlier versions of local (k0,k1)-isomorphisms and use the most simplified local (k0,k1)-isomorphism. This approach is indeed a key step to make the axioms for a digital covering space very refined. In this paper, the most refined local (k0,k1)-isomorphism is proved to be a (k0,k1)-covering map, which implies that the earlier axioms for a digital covering space are significantly simplified with one axiom. This finding facilitates the calculations of digital fundamental groups of digital images using the unique lifting property and the homotopy lifting theorem. In addition, consider a simple closed k:=k(t,n)-curve with five elements in Zn, denoted by SCkn,5. After introducing the notion of digital topological imbedding, we investigate some properties of SCkn,5, where k:=k(t,n),3tn. Since SCkn,5 is the minimal and simple closed k-curve with odd elements in Zn which is not k-contractible, we strongly study some properties of it associated with generalized digital wedges from the viewpoint of fixed point theory. Finally, after introducing the notion of generalized digital wedge, we further address some issues which remain open. The present paper only deals with k-connected digital images. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
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Article
Local Sharp Vector Variational Type Inequality and Optimization Problems
Mathematics 2020, 8(10), 1844; https://doi.org/10.3390/math8101844 - 20 Oct 2020
Viewed by 531
Abstract
In this paper, our goal was to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, [...] Read more.
In this paper, our goal was to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate η-convexity conditions for locally Lipschitzian functions. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
Article
Linear Convergence of Split Equality Common Null Point Problem with Application to Optimization Problem
Mathematics 2020, 8(10), 1836; https://doi.org/10.3390/math8101836 - 19 Oct 2020
Viewed by 428
Abstract
The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in [...] Read more.
The purpose of this paper is to propose an iterative algorithm for solving the split equality common null point problem (SECNP), which is to find an element of the set of common zero points for a finite family of maximal monotone operators in Hilbert spaces. We introduce the concept of bounded linear regularity for the SECNP and construct several sufficient conditions to ensure the linear convergence of the algorithm. Moreover, some numerical experiments are given to test the validity of our results. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
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Article
Fixed Point Sets of k-Continuous Self-Maps of m-Iterated Digital Wedges
Mathematics 2020, 8(9), 1617; https://doi.org/10.3390/math8091617 - 18 Sep 2020
Cited by 2 | Viewed by 542
Abstract
Let Ckn,l be a simple closed k-curves with l elements in Zn and W:=Ckn,lCkn,lm-times be an m-iterated digital wedges of Ckn,l, and F(Conk(W)) be an alignment of fixed point sets of W. Then, the aim of the paper is devoted to investigating various properties of F(Conk(W)). Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of Ckn,l, denoted by F(Conk(Ckn,l)), where l(7) is an odd natural number and k2n. Secondly, given a digital image (X,k) with X=n, we find a certain condition that supports n1,n2F(Conk(X)). Thirdly, after finding some features of F(Conk(W)), we develop a method of making F(Conk(W)) perfect according to the (even or odd) number l of Ckn,l. Finally, we prove that the perfectness of F(Conk(W)) is equivalent to that of F(Conk(Ckn,l)). This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k-connected digital images (X,k) such that X2. Full article
(This article belongs to the Special Issue Nonlinear Problems and Applications of Fixed Point Theory)
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