Special Issue "Fixed Point Theory and Related Topics"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 January 2020

Special Issue Editor

Guest Editor
Prof. Dr. Hsien-Chung Wu

Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Website | E-Mail
Interests: fuzzy optimization; fuzzy real analysis; fuzzy statistical analysis; operations research; computational intelligence; soft computing; fixed point theory; applied functional analysis

Special Issue Information

Dear Colleagues,

Fixed point theory arose from the Banach contraction principle and has been studied for a long time. Its application mostly relies on the existence of solutions to mathematical problems that are formulated from economics and engineering. After the existence of the solutions is guaranteed, the numerical methodology will be established to obtain the approximated solution. Fixed points of function depend heavily on the considered spaces that are defined using the intuitive axioms. In particular, variant metrics spaces are proposed, like a partial metric space, b-metric space, fuzzy metric space and probabilistic metric space, etc. Different spaces will result in different types of fixed point theorems. In other words, there are a lot of different types of fixed point theorems in the literature. Therefore, this Special Issue welcomes survey articles. Articles that unify the different types of fixed point theorems are also very welcome. The topics of this Special Issue include:

  • fixed point theorems in metric space
  • fixed point theorems in fuzzy metric space
  • fixed point theorems in probabilistic metric space
  • fixed point theorems of set-valued functions in various spaces
  • the existence of solutions in game theory
  • the existence of solutions for equilibrium problems
  • the existence of solutions of differential equations
  • the existence of solutions of integral equations
  • numerical methods for obtaining the approximated fixed points

Prof. Dr. Hsien-Chung Wu
Guest Editor

Manuscript Submission Information

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Keywords

  • Fixed Point
  • Best Proximity Point
  • Equilibrium
  • Cauchy Sequences
  • Completeness
  • Game Theory

Published Papers (4 papers)

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Research

Open AccessArticle
Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application
Received: 11 March 2019 / Revised: 17 April 2019 / Accepted: 18 April 2019 / Published: 24 April 2019
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Abstract
In this paper, by introducing the concept of generalized Ćirić-type weak (ϕg,R)-contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R. We also deduce some useful consequences showing the [...] Read more.
In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics)
Open AccessArticle
Applications of Square Roots of Diffeomorphisms
Received: 9 March 2019 / Revised: 8 April 2019 / Accepted: 9 April 2019 / Published: 11 April 2019
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Abstract
In this paper, we prove that on any contact manifold (M,ξ) there exists an arbitrary C-small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C-small contactomorphism which is not [...] Read more.
In this paper, we prove that on any contact manifold ( M , ξ ) there exists an arbitrary C -small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C -small contactomorphism which is not “autonomous”. This paper is the first step to study the topology of C o n t 0 ( M , ξ ) Aut ( M , ξ ) . As an application, we also prove a similar result for the diffeomorphism group Diff ( M ) for any smooth manifold M. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics)
Open AccessArticle
Fixed Point Theorems for Geraghty Contraction Type Mappings in b-Metric Spaces and Applications
Received: 8 February 2019 / Revised: 7 March 2019 / Accepted: 12 March 2019 / Published: 14 March 2019
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Abstract
In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral [...] Read more.
In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral equations are also given. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics)
Open AccessArticle
Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph
Received: 3 January 2019 / Revised: 23 January 2019 / Accepted: 28 January 2019 / Published: 1 February 2019
Cited by 2 | PDF Full-text (652 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we ensure the existence and uniqueness of a best proximity point in rectangular metric spaces endowed with a graph structure. Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Topics)
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