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Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and...
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Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 4791

Special Issue Editors

Prof. Dr. Wei-Shih Du

E-Mail Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis; fixed point theory and its applications; variational principles and inequalities; optimization theory; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals
Dr. Yousuke Araya

E-Mail Website
Guest Editor
Faculty of Systems Science and Technology, Akita Prefectural University, 84-4 Aza Ebinokuchi Tsuchiya, Yurihonjo City 015-0055, Akita, Japan
Interests: nonlinear analysis; robust optimization; equilibrium problem; set optimization; vector optimization and their applications

Special Issue Information

Dear Colleagues,

After more than a century of unremitting efforts by scholars, nonlinear analysis has found widespread and important applications in many fields that are at the core of many branches of pure and applied mathematics, including functional analysis, fixed point theory, nonlinear ordinary and partial differential equations, variational analysis, dynamical system theory, control theory, convex analysis, nonsmooth analysis, critical point theory, nonlinear optimization, fractional calculus and its applications, probability and statistics, mathematical economics, data mining, signal processing, biological engineering, electronic networks, electromagnetic theory, and so forth.

In the last century, optimization problems have been intensively studied and various iterative methods have been proposed. Many problems that arise in the real world are solved using different optimization algorithms and techniques via mathematical models. Among the possible application fields of optimization, we note integral and differential equations and inclusions, dynamic system theory, control theory, economics, game theory, machine learning, clustering, location theory, game theory, signal processing, finance mathematics, and so on. The construction and processing of artificial intelligence (AI) models has been one of the hottest optimization research topics over the past fifty years. Algorithms play an important role in optimization and its applications. The proposal of various feasible optimization algorithms has promoted the progress of artificial intelligence.

We cordially and earnestly invite researchers to contribute their original and high-quality research papers related to the advanced novel methods and algorithms for fixed point theory, optimization and their applications. Potential topics include, but are not limited to:

  • Fixed point theory and best proximity point theory;
  • Convex and nonconvex optimization problems;
  • Fractional integro-differential equations;
  • Algorithms;
  • Vector optimization problems;
  • Set-valued optimization problems;
  • Matrix theory;
  • Numerical analysis;
  • Control theory;
  • Finite element method;
  • Computational intelligence;
  • Linear and nonlinear dynamical systems;
  • Image and signal processing;
  • Inverse and ill-posed problems;
  • Machine learning;
  • Data analytics.

Prof. Dr. Wei-Shih Du
Dr. Yousuke Araya
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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
  • best proximity point theory
  • fractional integro-differential equation
  • finite element method
  • algorithms
  • vector optimization problems
  • set-valued optimization problems
  • dynamical system
  • computational intelligence
  • image and signal processing
  • inverse and ill-posed problems
  • convex and nonconvex optimization problems
  • machine learning
  • data analytics

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue polices can be found here.

Published Papers (6 papers)

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Research

21 pages, 343 KiB  
Article
Proximal Contractions for Multivalued Mappings with an Application to 2D Volterra Integral Equations
by Haroon Ahmad, Mudasir Younis, Hami Gündoǧdu, Nisha Barley and Vijay Kumar Patel
Mathematics 2024, 12(23), 3716; https://doi.org/10.3390/math12233716 - 27 Nov 2024
Viewed by 439
Abstract
In this paper, we delve into the ideas of Geraghty-type proximal contractions and their relation to multivalued, single-valued, and self mappings. We begin by introducing the notions of (ψω)MCP-proximal Geraghty contraction and rational [...] Read more.
In this paper, we delve into the ideas of Geraghty-type proximal contractions and their relation to multivalued, single-valued, and self mappings. We begin by introducing the notions of (ψω)MCP-proximal Geraghty contraction and rational (ψω)RMCP-proximal Geraghty contraction for multivalued mappings, aimed at establishing coincidence point results. To enhance our understanding and illustrate the concepts, practical examples are provided with each definition. This study extends these contractions to single-valued mappings with the introduction of (ψω)SCP-proximal Geraghty contraction and rational (ψω)RSCP-proximal Geraghty contraction, supported by relevant examples to reinforce the main results. Then, we explore (ψω)SFP Geraghty contraction and rational (ψω)RSFP contraction for self-mappings, obtaining fixed point theorems and clearly illustrating them through examples. Finally, we apply the theoretical framework developed to investigate the existence and uniqueness of solutions to certain two-dimensional Volterra integral equations. Specifically, we consider the transformation of first-kind Volterra integral equations, which play crucial roles in modeling memory in diverse scientific fields like biology, physics, and engineering. This approach provides a powerful tool for solving difficult integral equations and furthering applied mathematics research. Full article
(This article belongs to the Special Issue Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications)
21 pages, 471 KiB  
Article
Some Results on Multivalued Proximal Contractions with Application to Integral Equation
by Muhammad Zahid, Fahim Ud Din, Mudasir Younis, Haroon Ahmad and Mahpeyker Öztürk
Mathematics 2024, 12(22), 3488; https://doi.org/10.3390/math12223488 - 7 Nov 2024
Viewed by 600
Abstract
In this manuscript, for the purpose of investigating the coincidence best proximity point, best proximity point, and fixed point results via alternating distance ϕ, we discuss some multivalued (ϕ−Fτ)CP and [...] Read more.
In this manuscript, for the purpose of investigating the coincidence best proximity point, best proximity point, and fixed point results via alternating distance ϕ, we discuss some multivalued (ϕ−Fτ)CP and (ϕ−Fτ)BP−proximal contractions in the context of rectangular metric spaces. To ascertain the coincidence best proximity point, best proximity point, and the fixed point for single-valued mappings, we reduce these findings using (Fτ)CP and (Fτ)BP−proximal contractions. To make our work more understandable, examples of both single- and multivalued mappings are provided. These examples support our core findings, which rely on coincidence points, as well as the corollaries that address fixed point conclusions. In the final phase of our study, we use the obtained results to verify that a solution to a Fredholm integral equation exists. This application highlights the theoretical framework we built throughout our study. Full article
(This article belongs to the Special Issue Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications)
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14 pages, 652 KiB  
Article
Convergence of Graph-Based Fixed Point Results with Application to Fredholm Integral Equation
by Haroon Ahmad, Aqsa Riaz, Mahpeyker Öztürk, Fahim Ud Din, Mehmet Emir Köksal and Ekber Girgin
Mathematics 2024, 12(20), 3226; https://doi.org/10.3390/math12203226 - 15 Oct 2024
Viewed by 528
Abstract
In this manuscript, we present a novel concept termed graphical Θc-Kannan contraction within the context of graphically controlled metric-type spaces. Unlike traditional Kannan contraction, this novel concept presents a modified method of contraction mapping. We discuss the significance and the existence [...] Read more.
In this manuscript, we present a novel concept termed graphical Θc-Kannan contraction within the context of graphically controlled metric-type spaces. Unlike traditional Kannan contraction, this novel concept presents a modified method of contraction mapping. We discuss the significance and the existence of fixed point results within the framework of this novel contraction. To strengthen the credibility of our theoretical remarks, we provide a comparison example demonstrating the efficiency of our suggested framework. Our study not only broadens the theoretical foundations inside graphically controlled metric-type spaces by introducing and examining visual Θc-Kannan contraction, but it also demonstrates the practical significance of our innovations through significant examples. Furthermore, applying our findings to second-order differential equations by constructing integral equations into the domain of Fredholm sheds light on the broader implications of our research in the field of mathematical analysis and contributes to the advancement of this field. Full article
(This article belongs to the Special Issue Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications)
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16 pages, 856 KiB  
Article
An Inertial Relaxed CQ Algorithm with Two Adaptive Step Sizes and Its Application for Signal Recovery
by Teeranush Suebcharoen, Raweerote Suparatulatorn, Tanadon Chaobankoh, Khwanchai Kunwai and Thanasak Mouktonglang
Mathematics 2024, 12(15), 2406; https://doi.org/10.3390/math12152406 - 2 Aug 2024
Viewed by 649
Abstract
This article presents a novel inertial relaxed CQ algorithm for solving split feasibility problems. Note that the algorithm incorporates two adaptive step sizes here. A strong convergence theorem is established for the problem under some standard conditions. Additionally, we explore the utility of [...] Read more.
This article presents a novel inertial relaxed CQ algorithm for solving split feasibility problems. Note that the algorithm incorporates two adaptive step sizes here. A strong convergence theorem is established for the problem under some standard conditions. Additionally, we explore the utility of the algorithm in solving signal recovery problems. Its performance is evaluated against existing techniques from the literature. Full article
(This article belongs to the Special Issue Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications)
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14 pages, 316 KiB  
Article
Local Second Order Sobolev Regularity for p-Laplacian Equation in Semi-Simple Lie Group
by Chengwei Yu and Yue Zeng
Mathematics 2024, 12(4), 601; https://doi.org/10.3390/math12040601 - 17 Feb 2024
Viewed by 921
Abstract
In this paper, we establish a structural inequality of the ∞-subLaplacian ▵0,∞ in a class of the semi-simple Lie group endowed with the horizontal vector fields X1,…,X2n. When [...] Read more.
In this paper, we establish a structural inequality of the ∞-subLaplacian ▵0,∞ in a class of the semi-simple Lie group endowed with the horizontal vector fields X1,…,X2n. When 1<p≤4 with n=1 and 1<p<3+1n−1 with n≥2, we apply the structural inequality to obtain the local horizontal W2,2-regularity of weak solutions to p-Laplacian equation in the semi-simple Lie group. Compared to Euclidean spaces R2n with n≥2, the range of this p obtained is already optimal. Full article
(This article belongs to the Special Issue Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications)
14 pages, 291 KiB  
Article
Generalized Almost Periodicity in Measure
by Marko Kostić, Wei-Shih Du, Halis Can Koyuncuoğlu and Daniel Velinov
Mathematics 2024, 12(4), 548; https://doi.org/10.3390/math12040548 - 10 Feb 2024
Cited by 1 | Viewed by 788
Abstract
This paper investigates diverse classes of multidimensional Weyl and Doss ρ-almost periodic functions in a general measure setting. This study establishes the fundamental structural properties of these generalized ρ-almost periodic functions, extending previous classes such as m-almost periodic and (equi-)Weyl- [...] Read more.
This paper investigates diverse classes of multidimensional Weyl and Doss ρ-almost periodic functions in a general measure setting. This study establishes the fundamental structural properties of these generalized ρ-almost periodic functions, extending previous classes such as m-almost periodic and (equi-)Weyl-p-almost periodic functions. Notably, a new class of (equi-)Weyl-p-almost periodic functions is introduced, where the exponent p>0 is general. This paper delves into the abstract Volterra integro-differential inclusions, showcasing the practical implications of the derived results. This work builds upon the extensions made in the realm of Levitan N-almost periodic functions, contributing to the broader understanding of mathematical functions in diverse measure spaces. Full article
(This article belongs to the Special Issue Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications)
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