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Symmetry
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Nonlinear Analysis and Its Applications in Symmetry II
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Nonlinear Analysis and Its Applications in Symmetry II

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

Deadline for manuscript submissions: 30 September 2024 | Viewed by 6327

Special Issue Editor

Dr. Alexander Zaslavski

E-Mail Website
Guest Editor
Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Interests: variational and optimal control problems on unbounded domains; optimization theory and related topics; infinite products of operators and their applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue of Symmetry is devoted to recent advances in non-linear analysis and its applications.

The growing significance of non-linear analysis and its applications has been realized in the recent years. This is due not only to theoretical achievements in this area, but also because of numerous applications to engineering, economics, biology, behavioral sciences, etc. It has become more and more evident that non-linear analysis is of crucial importance in the mathematical sciences. Its ideas and methods have turned out to be essential tools in the analysis of non-linear phenomena in many areas of mathematics. Among these areas, one can mention ordinary differential equations, partial differential equations, non-linear operator theory, the calculus of variations, optimal control theory, optimization, and mathematical economics.

Our aim is for this Special Issue to be valuable to mathematicians and applied scientists who are interested in recent developments in nonlinear analysis and its applications. Please note that all submitted papers must be within the general scope of the Symmetry journal.

Prof. Dr. Alexander Zaslavski 
Guest Editor

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

  • symmetry analysis
  • symmetry/asymmetry phenomena
  • symmetry nonlinear system
  • symmetry and fixed point
  • complete metric space
  • contractive mapping
  • iterate
  • nonexpansive mapping
  • set-valued mapping

Published Papers (6 papers)

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Research

16 pages, 283 KiB  
Article
Coupled Fixed Point Theory in Subordinate Semimetric Spaces
by Areej Alharbi, Maha Noorwali and Hamed H. Alsulami
Symmetry 2024, 16(4), 499; https://doi.org/10.3390/sym16040499 - 19 Apr 2024
Viewed by 218
Abstract
The aim of this paper is to study the coupled fixed point of a class of mixed monotone operators in the setting of a subordinate semimetric space. Using the symmetry between the subordinate semimetric space and a JS-space, we generalize the results of [...] Read more.
The aim of this paper is to study the coupled fixed point of a class of mixed monotone operators in the setting of a subordinate semimetric space. Using the symmetry between the subordinate semimetric space and a JS-space, we generalize the results of Senapati and Dey on JS-spaces. In this paper, we obtain some coupled fixed point results and support them with some examples. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
10 pages, 299 KiB  
Article
Examining Nonlinear Fredholm Equations in Lebesgue Spaces with Variable Exponents
by Mostafa Bachar, Mohamed A. Khamsi and Osvaldo Méndez
Symmetry 2023, 15(11), 2014; https://doi.org/10.3390/sym15112014 - 02 Nov 2023
Viewed by 563
Abstract
We investigate the existence of solutions for the Fredholm integral equation Φ(ϑ)=G(ϑ,Φ(ϑ))+∫01F(ϑ,ζ,Φ(ζ))dζ, [...] Read more.
We investigate the existence of solutions for the Fredholm integral equation Φ(ϑ)=G(ϑ,Φ(ϑ))+∫01F(ϑ,ζ,Φ(ζ))dζ, for ϑ∈[0,1], in the setting of the modular function spaces Lρ. We also derive an application of this research within the framework of variable exponent Lebesgue spaces Lp(·) subject to specific conditions imposed on the exponent function p(·) and the functions F and G. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
7 pages, 231 KiB  
Article
Three Convergence Results for Inexact Iterates of Uniformly Locally Nonexpansive Mappings
by Simeon Reich and Alexander J. Zaslavski
Symmetry 2023, 15(5), 1084; https://doi.org/10.3390/sym15051084 - 15 May 2023
Cited by 2 | Viewed by 737
Abstract
In 2006, together with D. Butnariu, we showed that if all iterates of a nonexpansive self-mapping of a complete metric space converge, then all its inexact iterates with summable computational errors converge too. In a recent paper of ours, we have extended this [...] Read more.
In 2006, together with D. Butnariu, we showed that if all iterates of a nonexpansive self-mapping of a complete metric space converge, then all its inexact iterates with summable computational errors converge too. In a recent paper of ours, we have extended this result to uniformly locally nonexpansive self-mappings of a complete metric space. In the present paper, we establish analogous results for uniformly locally nonexpansive mappings which take a nonempty closed subset of a complete metric space into the space. In the particular case of a Banach space, if the operator is symmetric, then the set of all limit points of its iterates is also symmetric. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
16 pages, 319 KiB  
Article
Existence and Nonexistence of Positive Solutions for Perturbations of the Anisotropic Eigenvalue Problem
by Olena Andrusenko, Leszek Gasiński and Nikolaos S. Papageorgiou
Symmetry 2023, 15(2), 495; https://doi.org/10.3390/sym15020495 - 13 Feb 2023
Viewed by 780
Abstract
We consider a Dirichlet problem, which is a perturbation of the eigenvalue problem for the anisotropic p-Laplacian. We assume that the perturbation is (p(z)−1)-sublinear, and we prove an existence and nonexistence theorem for positive [...] Read more.
We consider a Dirichlet problem, which is a perturbation of the eigenvalue problem for the anisotropic p-Laplacian. We assume that the perturbation is (p(z)−1)-sublinear, and we prove an existence and nonexistence theorem for positive solutions as the parameter λ moves on the positive semiaxis. We also show the existence of a smallest positive solution and determine the monotonicity and continuity properties of the minimal solution map. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
26 pages, 646 KiB  
Article
Improvement of Unconstrained Optimization Methods Based on Symmetry Involved in Neutrosophy
by Predrag S. Stanimirović, Branislav Ivanov, Dragiša Stanujkić, Vasilios N. Katsikis, Spyridon D. Mourtas, Lev A. Kazakovtsev and Seyyed Ahmad Edalatpanah
Symmetry 2023, 15(1), 250; https://doi.org/10.3390/sym15010250 - 16 Jan 2023
Cited by 4 | Viewed by 1502
Abstract
The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we [...] Read more.
The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Moré performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
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18 pages, 569 KiB  
Article
Descent Derivative-Free Method Involving Symmetric Rank-One Update for Solving Convex Constrained Nonlinear Monotone Equations and Application to Image Recovery
by Aliyu Muhammed Awwal, Adamu Ishaku, Abubakar Sani Halilu, Predrag S. Stanimirović, Nuttapol Pakkaranang and Bancha Panyanak
Symmetry 2022, 14(11), 2375; https://doi.org/10.3390/sym14112375 - 10 Nov 2022
Cited by 1 | Viewed by 1127
Abstract
Many practical applications in applied sciences such as imaging, signal processing, and motion control can be reformulated into a system of nonlinear equations with or without constraints. In this paper, a new descent projection iterative algorithm for solving a nonlinear system of equations [...] Read more.
Many practical applications in applied sciences such as imaging, signal processing, and motion control can be reformulated into a system of nonlinear equations with or without constraints. In this paper, a new descent projection iterative algorithm for solving a nonlinear system of equations with convex constraints is proposed. The new approach is based on a modified symmetric rank-one updating formula. The search direction of the proposed algorithm mimics the behavior of a spectral conjugate gradient algorithm where the spectral parameter is determined so that the direction is sufficiently descent. Based on the assumption that the underlying function satisfies monotonicity and Lipschitz continuity, the convergence result of the proposed algorithm is discussed. Subsequently, the efficiency of the new method is revealed. As an application, the proposed algorithm is successfully implemented on image deblurring problem. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Its Applications in Symmetry II)
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