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

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 December 2024 | Viewed by 1380

Special Issue Editors


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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

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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

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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

Published Papers (2 papers)

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Research

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 539
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<p4 with n=1 and 1<p<3+1n1 with n2, 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 n2, the range of this p obtained is already optimal. Full article
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
Viewed by 495
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
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