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Mathematics
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Applied Functional Analysis and Applications: 2nd Edition
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Applied Functional Analysis and Applications: 2nd Edition

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

Deadline for manuscript submissions: 20 January 2025 | Viewed by 4293

Special Issue Editor

Prof. Dr. Jen-Chih Yao

E-Mail Website
Guest Editor
1. Research Center for Interneural Computing, China Medical University Hospital, Taichung City 404332, Taiwan
2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
Interests: vector optimization; fixed point theory; variational inequalities; complementarity problems; variational analysis; equilibrium problems; optimal control; generalized convexity and generalized monotonicity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Applied functional analysis is vital in most applied research fields; moreover, its influence has grown in recent decades. Indeed, most novel papers seem to have used the techniques, ideas, notions, and methods of applied functional analysis. Applied functional analysis includes linear and nonlinear problems from numerical analysis, systems theory, calculus of variations, control and optimization theory, convex and non-smooth analysis, and more.

This Special Issue deals mainly with theoretical functional analysis approaches to mathematical problems that are related to the real world. Any significant area of the application of functional analysis, such as new developments in functional analysis and contributions to important problems in and challenges to functional analysis, are welcome. We also accept high-quality research or review papers focusing on problems that arise from linear, nonlinear, conic, stochastic, discrete, and dynamic optimization, as well as variational and convex analysis.

The purpose of this Special Issue is to connect the efforts of mathematicians, engineers, and other scientists for whom applied functional analysis is important for research.

Prof. Dr. Jen-Chih Yao
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. 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

  • convex and non-convex optimization
  • variational problems
  • bilevel optimization problems
  • quasi-variational inequalities
  • numerical analysis for optimization problems
  • monotone inclusion problems
  • nonlinear integral equations
  • fixed point theory
  • variational inequalities
  • Hilbert spaces
  • Banach spaces

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Related Special Issue

Published Papers (6 papers)

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Research

10 pages, 281 KiB  
Article
Relational Strict Almost Contractions Employing Test Functions and an Application to Nonlinear Integral Equations
by Doaa Filali and Faizan Ahmad Khan
Mathematics 2024, 12(20), 3262; https://doi.org/10.3390/math12203262 - 17 Oct 2024
Viewed by 510
Abstract
The present study deals with some fixed-point outcomes under a nonlinear formulation of strict almost contractions in a metric space endued with an arbitrary relation. The outcomes established herein enhance and develop various existing outcomes. To convince you of the infallibility of our [...] Read more.
The present study deals with some fixed-point outcomes under a nonlinear formulation of strict almost contractions in a metric space endued with an arbitrary relation. The outcomes established herein enhance and develop various existing outcomes. To convince you of the infallibility of our outcomes, a few examples are presented. We apply our findings to investigate the validity of the unique solution of a nonlinear integral problem. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
17 pages, 301 KiB  
Article
A Projection-Type Implicit Algorithm for Finding a Common Solution for Fixed Point Problems and Variational Inequality Problems
by Vasile Berinde
Mathematics 2024, 12(20), 3187; https://doi.org/10.3390/math12203187 - 11 Oct 2024
Viewed by 606
Abstract
This paper deals with the problem of finding a common solution for a fixed point problem for strictly pseudocontractive mappings and for a certain variational inequality problem. We propose a projection-type implicit averaged algorithm and establish the strong convergence of the sequences generated [...] Read more.
This paper deals with the problem of finding a common solution for a fixed point problem for strictly pseudocontractive mappings and for a certain variational inequality problem. We propose a projection-type implicit averaged algorithm and establish the strong convergence of the sequences generated by this method to the common solution for the fixed point problem and the variational inequality problem. In order to illustrate the feasibility of the hypotheses and the superiority of our theoretical results over the existing literature, an example is also presented. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
30 pages, 1729 KiB  
Article
Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric
by Himanshu Baranwal, Ravindra Kishor Bisht, Arya Kumar Bedabrata Chand and Jen-Chih Yao
Mathematics 2024, 12(18), 2877; https://doi.org/10.3390/math12182877 - 15 Sep 2024
Viewed by 790
Abstract
This paper explores fixed points for both contractive and non-contractive mappings in traditional b-metric spaces, preordered b-metric spaces, and random b-metric spaces. Our findings provide insights into the behavior of mappings under various constraints and extend our approach to include [...] Read more.
This paper explores fixed points for both contractive and non-contractive mappings in traditional b-metric spaces, preordered b-metric spaces, and random b-metric spaces. Our findings provide insights into the behavior of mappings under various constraints and extend our approach to include coincidence and common fixed-point theorems in these spaces. We present new examples and graphical representations for the first time, offering novel results and enhancing several related findings in the literature, while broadening the scope of earlier works of Ran and Reurings, Nieto and Rodríguez-López, Górnicki, and others. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
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14 pages, 289 KiB  
Article
A Minimax-Program-Based Approach for Robust Fractional Multi-Objective Optimization
by Henan Li, Zhe Hong and Do Sang Kim
Mathematics 2024, 12(16), 2475; https://doi.org/10.3390/math12162475 - 10 Aug 2024
Viewed by 541
Abstract
In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of [...] Read more.
In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of generalized convex functions. Additionally, we formulate a dual problem to the primal one and examine duality relations between them. In our results, by using the obtained results, we obtain necessary and sufficient optimality conditions for a class of robust fractional multi-objective optimization problems. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
30 pages, 2131 KiB  
Article
Multidimensional Evolution Effects on Non-Cooperative Strategic Games
by Shipra Singh, Aviv Gibali and Simeon Reich
Mathematics 2024, 12(16), 2453; https://doi.org/10.3390/math12162453 - 7 Aug 2024
Viewed by 773
Abstract
In this study, we examine how the strategies of the players over multiple time scales impact the decision making, resulting payoffs and the costs in non-cooperative strategic games. We propose a dynamic generalized Nash equilibrium problem for non-cooperative strategic games which evolve in [...] Read more.
In this study, we examine how the strategies of the players over multiple time scales impact the decision making, resulting payoffs and the costs in non-cooperative strategic games. We propose a dynamic generalized Nash equilibrium problem for non-cooperative strategic games which evolve in multidimensions. We also define an equivalent dynamic quasi-variational inequality problem. The existence of equilibria is established, and a spot electricity market problem is reformulated in terms of the proposed dynamic generalized Nash equilibrium problem. Employing the theory of projected dynamical systems, we illustrate our approach by applying it to a 39-bus network case, which is based on the New England system. Moreover, we illustrate a comparative study between multiple time scales and a single time scale by a simple numerical experiment. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
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6 pages, 201 KiB  
Article
About the Subgradient Method for Equilibrium Problems
by Abdellatif Moudafi
Mathematics 2024, 12(13), 2081; https://doi.org/10.3390/math12132081 - 2 Jul 2024
Viewed by 530
Abstract
Convergence results of the subgradient algorithm for equilibrium problems were mainly obtained using a Lipschitz continuity assumption on the given bifunctions. In this paper, we first provide a complexity result for monotone equilibrium problems without assuming Lipschitz continuity. Moreover, we give a convergence [...] Read more.
Convergence results of the subgradient algorithm for equilibrium problems were mainly obtained using a Lipschitz continuity assumption on the given bifunctions. In this paper, we first provide a complexity result for monotone equilibrium problems without assuming Lipschitz continuity. Moreover, we give a convergence result of the value of the averaged sequence of iterates beyond Lipschitz continuity. Next, we derive a rate convergence in terms of the distance to the solution set relying on a growth condition. Applications to convex minimization and min–max problems are also stated. These ideas and results deserve to be developed and further refined. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
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