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Symmetry
Special Issues
Symmetry in Fixed Point Theory and Applications
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Symmetry in Fixed Point Theory and Applications

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

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 5780

Special Issue Editors

Dr. Vahid Parvaneh

E-Mail Website
Guest Editor
Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
Interests: fixed point theory; measure of non-compactness; nonlinear analysis
Prof. Dr. Bipan Hazarika

E-Mail Website
Guest Editor
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
Interests: sequence spaces; application of fixed point theory; measure of non-compactness; fractional calculus; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals
Dr. J.R. Roshan

E-Mail Website
Guest Editor
Department of Mathematics, Qaemshahr Branch, IslamicAzad University, Qaemshahr, Iran
Interests: fixed point theory; measure of non-compactness; nonlinear analysis; fractional calculus; nonlinear matrix equations
Dr. Pradip Debnath

E-Mail Website
Guest Editor
Department of Applied Science and Humanities, Assam University, Silchar, India
Interests: nonlinear functional analysis; fixed point theory; decision making; soft computing; mathematical statistics

Special Issue Information

Dear Colleagues,

There are various types of differential and integral equations that arise from problems in engineering, physics, chemistry, and economics, among others. The existence and uniqueness of these equations' solutions have always been major concerns for researchers. The theorems of fixed point and the measure of non-compactness are potent tools for demonstrating the existence and uniqueness of numerous equations of this type. These equations may also be fractional differential equations, fractional integral equations, fractional differential inclusions, or fractional integral inclusions. Numerous researchers are interested in the existence and uniqueness of solutions for systems of differential equations, integral equations, and their fractional types. In addition, many authors are interested in non-compactness measures for numerous Banach spaces.

The aim of this Special Issue of Symmetry is to present some new developments in fixed point theory, the related non-linear problems, measures of non-compactness in different Banach spaces and Banach algebras, and symmetry applications. Our Guest Editor will accept very high-quality papers that contain original results and survey articles of exceptional merit. We invite you to contribute to the Special Issue "Symmetry in Fixed Point Theory and Applications" at https://www.mdpi.com/journal/symmetry/special_issues.

Dr. Vahid Parvaneh
Prof. Dr. Bipan Hazarika
Dr. J.R. Roshan
Dr. Pradip Debnath
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 submissions that pass pre-check are 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. Symmetry 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 2400 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
  • generalized contractive mapping
  • generalized metric spaces
  • solvability of integral equations
  • numerical algorithms for non-linear problems
  • well-posedness in fixed point theory
  • functional equations
  • differential and integral equations
  • differential and integral inclusions
  • fractional differential and integral equations
  • fractional differential and integral inclusions
  • systems of fractional differential and integral equations
  • systems of fractional differential and integral inclusions
  • symmetry

Published Papers (6 papers)

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Research

18 pages, 333 KiB  
Article
On Graphical Symmetric Spaces, Fixed-Point Theorems and the Existence of Positive Solution of Fractional Periodic Boundary Value Problems
by Nikita Dubey, Satish Shukla and Rahul Shukla
Symmetry 2024, 16(2), 182; https://doi.org/10.3390/sym16020182 - 03 Feb 2024
Viewed by 1074
Abstract
The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for H-(ϑ,φ)-contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equipped with [...] Read more.
The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for H-(ϑ,φ)-contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equipped with a function which characterizes the distance between two points of the space. Some topological properties of graphical symmetric spaces are discussed. Some fixed-point results for the mappings defined on graphical symmetric spaces are proved. The fixed-point results of this paper generalize and extend several fixed-point results in this new setting. The main results of this paper are applied to obtain the positive solutions of fractional periodic boundary value problems. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Applications)
13 pages, 298 KiB  
Article
Fixed Point Theory in Extended Parametric Sb-Metric Spaces and Its Applications
by Naveen Mani, Sunil Beniwal, Rahul Shukla and Megha Pingale
Symmetry 2023, 15(12), 2136; https://doi.org/10.3390/sym15122136 - 30 Nov 2023
Viewed by 772
Abstract
This article introduces the novel concept of an extended parametric Sb-metric space, which is a generalization of both Sb-metric spaces and parametric Sb-metric spaces. Within this extended framework, we first establish an analog version of the Banach [...] Read more.
This article introduces the novel concept of an extended parametric Sb-metric space, which is a generalization of both Sb-metric spaces and parametric Sb-metric spaces. Within this extended framework, we first establish an analog version of the Banach fixed-point theorem for self-maps. We then prove an improved version of the Banach contraction principle for symmetric extended parametric Sb-metric spaces, using an auxiliary function to establish the desired result. Finally, we provide illustrative examples and an application for determining solutions to Fredholm integral equations, demonstrating the practical implications of our work. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Applications)
11 pages, 273 KiB  
Article
Some Fixed-Point Results in Extended S-Metric Space of Type (α,β)
by Reham Qaralleh, Abdalla Tallafha and Wasfi Shatanawi
Symmetry 2023, 15(9), 1790; https://doi.org/10.3390/sym15091790 - 19 Sep 2023
Cited by 1 | Viewed by 788
Abstract
In this paper, we introduce the notion of extended S-metric space of type (α,β). This extension is a generalization of S-metric space, defined by employing two functions instead of considering a constant in the second condition [...] Read more.
In this paper, we introduce the notion of extended S-metric space of type (α,β). This extension is a generalization of S-metric space, defined by employing two functions instead of considering a constant in the second condition of the S-metric space definition. Accordingly, we prove some fixed-point results and give some examples to illustrate the validity of our work, along with giving an application of the Fredholm integral equation. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Applications)
15 pages, 862 KiB  
Article
Inertial Viscosity Approximation Methods for General Split Variational Inclusion and Fixed Point Problems in Hilbert Spaces
by Chanjuan Pan and Kunyang Wang
Symmetry 2023, 15(8), 1502; https://doi.org/10.3390/sym15081502 - 28 Jul 2023
Viewed by 553
Abstract
The purpose of this paper is to find a common element of the fixed point set of a nonexpansive mapping and the set of solutions of the general split variational inclusion problem in symmetric Hilbert spaces by using the inertial viscosity iterative method. [...] Read more.
The purpose of this paper is to find a common element of the fixed point set of a nonexpansive mapping and the set of solutions of the general split variational inclusion problem in symmetric Hilbert spaces by using the inertial viscosity iterative method. Some strong convergence theorems of the proposed algorithm are demonstrated. As applications, we use our results to study the split feasibility problem and the split minimization problem. Finally, the numerical experiments are presented to illustrate the feasibility and effectiveness of our theoretical findings, and our results extend and improve many recent ones. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Applications)
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15 pages, 372 KiB  
Article
Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration
by Fatima M. Azmi and Salma Haque
Symmetry 2023, 15(7), 1403; https://doi.org/10.3390/sym15071403 - 11 Jul 2023
Cited by 1 | Viewed by 823
Abstract
Fixed point theory is a versatile mathematical theory that finds applications in a wide range of disciplines, including computer science, engineering, fractals, and even behavioral sciences. In this study, we propose triple controlled metric-like spaces as a generalization of controlled rectangular metric-like spaces. [...] Read more.
Fixed point theory is a versatile mathematical theory that finds applications in a wide range of disciplines, including computer science, engineering, fractals, and even behavioral sciences. In this study, we propose triple controlled metric-like spaces as a generalization of controlled rectangular metric-like spaces. By examining the Θ-contraction mapping within these spaces, we extend and enhance the existing literature to establish significant fixed point results. Utilizing these findings, we demonstrate the existence of solutions to a Fredholm integral equation and provide an example of a numerical iteration method applicable to a specific case of this Fredholm integral equation. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Applications)
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18 pages, 348 KiB  
Article
On Relational Weak Fℜm,η-Contractive Mappings and Their Applications
by Muhammad Tariq, Muhammad Arshad, Eskandar Ameer, Ahmad Aloqaily, Suhad Subhi Aiadi and Nabil Mlaiki
Symmetry 2023, 15(4), 922; https://doi.org/10.3390/sym15040922 - 15 Apr 2023
Cited by 2 | Viewed by 822
Abstract
In this article, we introduce the concept of weak Fℜm,η-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where η is a control function and ℜ is a relation. Then, we detail some fixed point results [...] Read more.
In this article, we introduce the concept of weak Fℜm,η-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where η is a control function and ℜ is a relation. Then, we detail some fixed point results for cyclic-type weak Fℜm,η-contraction mappings. Finally, we demonstrate some illustrative examples and discuss upper and lower solutions of Volterra-type integral equations of the form ξα=∫0αAα,σ,ξσmσ+Ψα,α∈0,1. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Theory and Applications)
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