Symmetric and non-symmetric contractions in various abstract spaces

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 May 2019) | Viewed by 6904

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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
Interests: functional analysis; operator theory; linear topological invariants; fixed point theory; best proximity
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Dear Colleagues,

Due to its possible applications, Metric Fixed Point Theory plays a key role in Nonlinear Analysis and one of the core topic for the researchers.

In the last fifty years, discussions on the existence and uniqueness of fixed points of single and multivalued operators in different kind of spaces (such as symmetric spaces, non-symmetric spaces, quasi-metric spaces, pseudo-quasi-metric spaces, partial metric spaces, b-metric spaces and dislocated metric spaces, Bianciari distance, among others) has attracted the attention of numerous researchers. The enormous potential of its applications to almost all quantitative sciences (such as Mathematics, Engineering, Chemistry, Biology, Economics, Computer Science, and others) justify the present great interest in this area. The purpose of this special issue is to collect recent advances and improvement in the symmetric spaces, non-symmetric spaces to present, share and open a new discussions on their main advances (ideas, techniques, possible results, proofs, etc.) in this area.

Prof. Dr. Erdal Karapinar
Guest Editor

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Keywords

  • Symmetric Spaces
  • Non-symmetric spaces
  • Quasi-metric spaces
  • Fixed point
  • Coincidence point
  • Common fixed point

Published Papers (2 papers)

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Research

10 pages, 771 KiB  
Article
The Meir–Keeler Fixed Point Theorem for Quasi-Metric Spaces and Some Consequences
by Salvador Romaguera and Pedro Tirado
Symmetry 2019, 11(6), 741; https://doi.org/10.3390/sym11060741 - 01 Jun 2019
Cited by 7 | Viewed by 2492
Abstract
We obtain quasi-metric versions of the famous Meir–Keeler fixed point theorem from which we deduce quasi-metric generalizations of Boyd–Wong’s fixed point theorem. In fact, one of these generalizations provides a solution for a question recently raised in the paper “On the fixed point [...] Read more.
We obtain quasi-metric versions of the famous Meir–Keeler fixed point theorem from which we deduce quasi-metric generalizations of Boyd–Wong’s fixed point theorem. In fact, one of these generalizations provides a solution for a question recently raised in the paper “On the fixed point theory in bicomplete quasi-metric spaces”, J. Nonlinear Sci. Appl. 2016, 9, 5245–5251. We also give an application to the study of existence of solution for a type of recurrence equations associated to certain nonlinear difference equations. Full article
(This article belongs to the Special Issue Symmetric and non-symmetric contractions in various abstract spaces)
17 pages, 332 KiB  
Article
Extended Rectangular b-Metric Spaces and Some Fixed Point Theorems for Contractive Mappings
by Zead Mustafa, Vahid Parvaneh, Mohammed M.M. Jaradat and Zoran Kadelburg
Symmetry 2019, 11(4), 594; https://doi.org/10.3390/sym11040594 - 24 Apr 2019
Cited by 20 | Viewed by 3564
Abstract
In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate [...] Read more.
In this paper, we introduce the class of extended rectangular b-metric spaces as a generalization of both rectangular metric and rectangular b-metric spaces. In addition, some fixed point results connected with certain contractions are obtained and examples are given to illustrate these results. Full article
(This article belongs to the Special Issue Symmetric and non-symmetric contractions in various abstract spaces)
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