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Symmetry
Special Issues
Symmetry in Nonlinear Analysis and Boundary Value Problems
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Symmetry in Nonlinear Analysis and Boundary Value Problems

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3137

Special Issue Editors

Prof. Dr. Wei-Shih Du

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Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Marko Kostić

E-Mail Website
Guest Editor
Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Interests: abstract Volterra integro-differential equations; abstract fractional differential equations; topological dynamics of linear operators and abstract PDEs
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Radu Precup

E-Mail Website
Guest Editor
Department of Mathematics, Babeş-Bolyai University, 400084 Cluj, Romania
Interests: nonlinear boundary value problems for ODEs and PDEs; theory of nonlinear operators; topological fixed point theory; critical point theory; mathematical modeling in biology and medicine
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Adrian Petrusel

E-Mail Website
Guest Editor
1. Faculty of Mathematics and Computer Science, Babeş-Bolyai University Cluj-Napoca, Mihail Kogălniceanu Street, no. 1, 400084 Cluj-Napoca, Romania
2. Academy of Romanian Scientists, Splaiul Independenţei Street, no. 54, Sector 5, RO-050094 Bucharest, Romania
Interests: fixed point theory; differential equations and integral equations; differential and integral inclusions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over the past century or more, nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, fixed point theory, nonlinear optimization, variational analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, signal processing, control theory, and so forth. Boundary value problems constitute a very important research topic in the theory of differential equations. As we all know, boundary value problems arise from the modeling of various phenomena in applied science and can be categorized as local and nonlocal, linear and nonlinear, posed and ill posed, singular and nonsingular, and free and fixed problems. 

This Special Issue will pay more attention to the new originality and applications of nonlinear analysis and boundary value problems in the real world, covering the widest range of symmetry. We cordially and earnestly invite researchers to contribute their original and high-quality research papers which will inspire advances in fixed point theory, computational analysis and their applications. Potential topics include but are not limited to:

Prof. Dr. Wei-Shih Du
Prof. Dr. Marko Kostić
Prof. Dr. Radu Precup
Prof. Dr. Adrian Petrusel
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

  • set-valued analysis
  • functional analysis
  • critical point theory
  • bifurcation theory
  • fixed point theory
  • fractional integro-differential equations
  • optimization
  • inverse and ill-posed problems
  • dynamical systems
  • image and signal processing

Published Papers (3 papers)

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Research

23 pages, 362 KiB  
Article
A New Accelerated Algorithm for Convex Bilevel Optimization Problems and Applications in Data Classification
by Panadda Thongpaen, Warunun Inthakon, Taninnit Leerapun and Suthep Suantai
Symmetry 2022, 14(12), 2617; https://doi.org/10.3390/sym14122617 - 10 Dec 2022
Cited by 1 | Viewed by 923
Abstract
In the development of algorithms for convex optimization problems, symmetry plays a very important role in the approximation of solutions in various real-world problems. In this paper, based on a fixed point algorithm with the inertial technique, we proposed and study a new [...] Read more.
In the development of algorithms for convex optimization problems, symmetry plays a very important role in the approximation of solutions in various real-world problems. In this paper, based on a fixed point algorithm with the inertial technique, we proposed and study a new accelerated algorithm for solving a convex bilevel optimization problem for which the inner level is the sum of smooth and nonsmooth convex functions and the outer level is a minimization of a smooth and strongly convex function over the set of solutions of the inner level. Then, we prove its strong convergence theorem under some conditions. As an application, we apply our proposed algorithm as a machine learning algorithm for solving some data classification problems. We also present some numerical experiments showing that our proposed algorithm has a better performance than the five other algorithms in the literature, namely BiG-SAM, iBiG-SAM, aiBiG-SAM, miBiG-SAM and amiBiG-SAM. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Boundary Value Problems)
15 pages, 330 KiB  
Article
Some Fixed Point Results in E-Metric Spaces and an Application
by Xinjie Shi, Pinhong Long, Huaping Huang and Fengjun Li
Symmetry 2022, 14(10), 2005; https://doi.org/10.3390/sym14102005 - 24 Sep 2022
Viewed by 1158
Abstract
The purpose of this paper is to study several fixed point problems in E-metric spaces. Mainly, we show the existence and uniqueness of fixed points for two contractive mappings, including Ćirić type contraction and α-ψ type contraction in E-metric [...] Read more.
The purpose of this paper is to study several fixed point problems in E-metric spaces. Mainly, we show the existence and uniqueness of fixed points for two contractive mappings, including Ćirić type contraction and α-ψ type contraction in E-metric spaces. Furthermore, we provide examples to support the accuracy of our results and present an application of our solution to a class of differential equations. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Boundary Value Problems)
27 pages, 430 KiB  
Article
Proportional Caputo Fractional Differential Inclusions in Banach Spaces
by Abdelkader Rahmani, Wei-Shih Du, Mohammed Taha Khalladi, Marko Kostić and Daniel Velinov
Symmetry 2022, 14(9), 1941; https://doi.org/10.3390/sym14091941 - 18 Sep 2022
Cited by 5 | Viewed by 1269
Abstract
In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order α∈(0,1) for a continuous (locally integrable) function u:[0,∞)→E, where E is a [...] Read more.
In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order α∈(0,1) for a continuous (locally integrable) function u:[0,∞)→E, where E is a complex Banach space. In our definition, we do not require that the function u(·) is continuously differentiable, which enables us to consider the wellposedness of the corresponding fractional relaxation problems in a much better theoretical way. More precisely, we systematically investigate several new classes of (degenerate) fractional solution operator families connected with the use of this type of fractional derivatives, obeying the multivalued linear approach to the abstract Volterra integro-differential inclusions. The quasi-periodic properties of the proportional fractional integrals as well as the existence and uniqueness of almost periodic-type solutions for various classes of proportional Caputo fractional differential inclusions in Banach spaces are also considered. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Boundary Value Problems)
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