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Symmetry
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Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations
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Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 4858

Special Issue Editors

Dr. Hasanen A. Hammad

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Guest Editor
Department of Mathematics, Sohag University, Sohag, Egypt
Interests: functional analysis; fixed point theory and its applications; optimizations; variational Inequalities; algorithms
Prof. Dr. Luis Manuel Sánchez Ruiz

E-Mail Website1 Website2
Guest Editor
ETSID-Department of Applied Mathematics, Universitat Politecnica de Valencia, 46022 Valencia, Spain
Interests: fractional calculus; analytical and computational methods; differential and difference equations; real and complex analysis; applied and computational mathematics; mathematical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many problems in science and engineering can be solved by reducing them to an equivalent fixed-point problem defined by nonlinear functional mathematical equations. In fact, an operator equation Tx = 0 may be expressed as a fixed-point equation Fx = x, where F is a self-mapping with some suitable domain. For example, split feasibility issues, variational inequality issues, nonlinear optimization issues, equilibrium issues, complementarity issues, selection and matching issues, and issues proving the existence of solutions to integral and differential equations can all be resolved using the fundamental tools provided by fixed-point theory. Fixed-point theorems are developed for single-valued or set-valued mappings of abstract metric spaces. In particular, the fixed-point theorems for set-valued mappings are rather advantageous in optimal control theory and have been frequently used to solve many problems of economics and game theory. On the other hand, in the case that F is non-self-mapping, the aforementioned equation does not necessarily have a fixed point. In such cases, it is worth determining an approximate solution x such that the error d(x; Fx) is minimum. This is the idea behind best approximation theory.

This Special Issue’s goal is to report on the most recent developments in problem-solving techniques, particularly those that make use of the fixed/best-proximity point theory. Such problems are typically studied in certain function spaces to see if they can be solved. The solvability of functional mathematical equations can be greatly influenced by the selection of the proper fixed/best-proximity point theorem and the use of particular characteristics of the underlying function space.

We want to give researchers a forum where they may communicate, discuss, and promote numerous fresh problems and advancements in this field. Possible subjects could include but are not limited to:

  • Fixed-point theory in various abstract spaces with applications;
  • Best proximity point theory in various abstract spaces with applications;
  • Nonlinear operator theory and applications;
  • Generalized contractive mappings;
  • Differential and integral equations by fixed-point theory;
  • Differential and integral inclusions by fixed-point theory;
  • Stability of functional equations related to fixed-point theory;
  • Fractional differential equations by fixed-point theory;
  • Fractional differential inclusions by fixed-point theory.

Dr. Hasanen A. Hammad
Prof. Dr. Luis Manuel Sánchez Ruiz
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 in various abstract spaces with applications
  • best proximity point theory in various abstract spaces with applications
  • nonlinear operator theory and applications
  • generalized contractive mappings
  • differential and integral equations by fixed-point theory
  • differential and integral inclusions by fixed-point theory
  • stability of functional equations related to fixed-point theory
  • fractional differential equations by fixed-point theory
  • fractional differential inclusions by fixed-point theory

Published Papers (7 papers)

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Research

15 pages, 352 KiB  
Article
Accelerated Subgradient Extragradient Algorithm for Solving Bilevel System of Equilibrium Problems
by Somyot Plubtieng and Tadchai Yuying
Symmetry 2023, 15(9), 1681; https://doi.org/10.3390/sym15091681 - 31 Aug 2023
Viewed by 771
Abstract
In this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant [...] Read more.
In this research paper, we propose a novel approach termed the inertial subgradient extragradient algorithm to solve bilevel system equilibrium problems within the realm of real Hilbert spaces. Our algorithm is capable of circumventing the necessity for prior knowledge about the Lipschitz constant of the involving bifunction and only computes the minimization of strong bifunctions onto the feasible set that is required. Under appropriate conditions, we establish strong convergence theorems for our proposed algorithms. To validate our algorithms, we illustrate a series of numerical examples. Through these examples, we demonstrate the performance of the algorithms we have put forth in this paper. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations)
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23 pages, 371 KiB  
Article
Solutions of Fractional Differential Inclusions and Stationary Points of Intuitionistic Fuzzy-Set-Valued Maps
by Monairah Alansari and Mohammed Shehu Shagari
Symmetry 2023, 15(8), 1535; https://doi.org/10.3390/sym15081535 - 03 Aug 2023
Viewed by 563
Abstract
One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point [...] Read more.
One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point results of crisp mappings have been improved by using the symmetry of metrics. However, more than a handful of fixed-point theorems in symmetric spaces are yet to be investigated in fuzzy versions. In accordance with the aforementioned orientation, the idea of Presic-type intuitionistic fuzzy stationary point results is introduced in this study within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed herein to complement their corresponding concepts related to multi-valued and single-valued mappings. In the instance where the intuitionistic fuzzy-set-valued map is reduced to its crisp counterparts, our results complement and generalize a few well-known fixed-point theorems with symmetric structure, including the main results of Banach, Ciric, Presic, Rhoades, and some others in the comparable literature. A significant number of consequences of our results in the set-up of fuzzy-set- and crisp-set-valued as well as point-to-point-valued mappings are emphasized and discussed. One of our findings is utilized to assess situations from the perspective of an application for the existence of solutions to non-convex fractional differential inclusions involving Caputo fractional derivatives with nonlocal boundary conditions. Some nontrivial examples are constructed to support the assertions and usability of our main ideas. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations)
22 pages, 452 KiB  
Article
Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications
by Hasanen A. Hammad and Doha A. Kattan
Symmetry 2023, 15(7), 1400; https://doi.org/10.3390/sym15071400 - 11 Jul 2023
Cited by 1 | Viewed by 1027
Abstract
In this study, we developed a new faster iterative scheme for approximate fixed points. This technique was applied to discuss some convergence and stability results for almost contraction mapping in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex [...] Read more.
In this study, we developed a new faster iterative scheme for approximate fixed points. This technique was applied to discuss some convergence and stability results for almost contraction mapping in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex Banach space. Moreover, some numerical experiments were investigated to illustrate the behavior and efficacy of our iterative scheme. The proposed method converges faster than symmetrical iterations of the S algorithm, Thakur algorithm and K* algorithm. Eventually, as an application, the nonlinear Volterra integral equation with delay was solved using the suggested method. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations)
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17 pages, 451 KiB  
Article
Advancements in Hybrid Fixed Point Results and F-Contractive Operators
by Rosemary O. Ogbumba, Mohammed Shehu Shagari, Monairah Alansari, Thwiba A. Khalid, Elsayed A. E. Mohamed and Awad A. Bakery
Symmetry 2023, 15(6), 1253; https://doi.org/10.3390/sym15061253 - 13 Jun 2023
Cited by 2 | Viewed by 686
Abstract
The aim of this manuscript is to introduce a novel concept called Jaggi-type hybrid (ϕ -F)-contraction and establish some fixed point results for this class of contractions in the framework of G-metric space. The validity of the main [...] Read more.
The aim of this manuscript is to introduce a novel concept called Jaggi-type hybrid (ϕ -F)-contraction and establish some fixed point results for this class of contractions in the framework of G-metric space. The validity of the main result is shown by a suitable example and the realized improvements with respect to the corresponding literature are highlighted. By using the constructed example, it is observed that the results established herein cannot be deduced from their analogs in previously announced results in the literature. As an application, the existence and uniqueness of solutions to certain nonlinear Volterra integral equations are investigated to illustrate the utility of our obtained results. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations)
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18 pages, 345 KiB  
Article
A New Viscosity Implicit Approximation Method for Solving Variational Inequalities over the Common Fixed Points of Nonexpansive Mappings in Symmetric Hilbert Space
by Linqi Sun, Hongwen Xu and Yan Ma
Symmetry 2023, 15(5), 1098; https://doi.org/10.3390/sym15051098 - 17 May 2023
Viewed by 847
Abstract
In this paper, based on the viscosity approximation method and the hybrid steepest-descent iterative method, a new implicit iterative algorithm is presented for finding the common fixed points set of a finite family of nonexpansive mappings in a reflexive Hilbert space, which is [...] Read more.
In this paper, based on the viscosity approximation method and the hybrid steepest-descent iterative method, a new implicit iterative algorithm is presented for finding the common fixed points set of a finite family of nonexpansive mappings in a reflexive Hilbert space, which is called a symmetric space. We prove that the sequence generated by this new implicit rule strongly converges to the unique solution of a class of variational inequalities under certain appropriate conditions of the parameters. Moreover, we also study the applications to a broader family of strictly pseudo-contractive mappings and generalized equilibrium problems that involve several variational inequality problems, optimization problems, and fixed-point problems. Finally, numerical results are provided to clarify the stability and effectiveness of the algorithm and to compare with some existing iterative algorithms. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations)
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19 pages, 313 KiB  
Article
Geometry and Application in Economics of Fixed Point
by Meena Joshi, Shivangi Upadhyay, Anita Tomar and Mohammad Sajid
Symmetry 2023, 15(3), 704; https://doi.org/10.3390/sym15030704 - 11 Mar 2023
Cited by 1 | Viewed by 1208
Abstract
Inspired by the reality that the collection of fixed/common fixed points can embrace any symmetrical geometric shape comparable to a disc, a circle, an elliptic disc, an ellipse, or a hyperbola, we investigate the subsistence of a fixed point and a common fixed [...] Read more.
Inspired by the reality that the collection of fixed/common fixed points can embrace any symmetrical geometric shape comparable to a disc, a circle, an elliptic disc, an ellipse, or a hyperbola, we investigate the subsistence of a fixed point and a common fixed point and study their geometry in a partial metric space by introducing some novel contractions and notions of a fixed ellipse-like curve and a common fixed ellipse-like curve which is symmetrical in shape but entirely different than that of an ellipse in a Euclidean space. We look at new hypotheses essential for the collection of nonunique fixed/common fixed points of some mathematical operators to incorporate an ellipse-like curve keeping in view the symmetry in fixed/common fixed points approaches. Appropriate nontrivial examples verify established conclusions. We conclude our work by applying our results to construct the mathematical model and solve the Production–Consumption Equilibrium problem of economics. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations)
17 pages, 321 KiB  
Article
Fixed Point Approaches for Multi-Valued Prešić Multi-Step Iterative Mappings with Applications
by Ali Raza, Mujahid Abbas, Hasanen A. Hammad and Manuel De la Sen
Symmetry 2023, 15(3), 686; https://doi.org/10.3390/sym15030686 - 09 Mar 2023
Viewed by 1040
Abstract
The purpose of this paper is to present some fixed point approaches for multi-valued Prešić k-step iterative-type mappings on a metric space. Furthermore, some corollaries are obtained to unify and extend many symmetrical results in the literature. Moreover, two examples are provided [...] Read more.
The purpose of this paper is to present some fixed point approaches for multi-valued Prešić k-step iterative-type mappings on a metric space. Furthermore, some corollaries are obtained to unify and extend many symmetrical results in the literature. Moreover, two examples are provided to support the main result. Ultimately, as potential applications, some contributions of integral type are investigated and the existence of a solution to the second-order boundary value problem (BVP) is presented. Full article
(This article belongs to the Special Issue Symmetry in Fixed Point Approaches and Nonlinear Functional Mathematical Equations)
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