Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Applied Functional Analysis and Applications: 2nd Edition
share announcement

Applied Functional Analysis and Applications: 2nd Edition

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

Deadline for manuscript submissions: 31 August 2025 | Viewed by 9066

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

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (11 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

17 pages, 300 KiB  
Article
A Novel Fixed-Point Iterative Process for Multivalued Mappings Applied in Solving a HIV Model of Fractional Order
by Rubayyi T. Alqahtani, Godwin Amechi Okeke and Cyril Ifeanyichukwu Ugwuogor
Mathematics 2025, 13(5), 739; https://doi.org/10.3390/math13050739 - 25 Feb 2025
Viewed by 397
Abstract
We introduce a new and a faster iterative method for the approximation of the fixed point of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We prove some stability and data-dependence results for this novel iterative scheme. A series of [...] Read more.
We introduce a new and a faster iterative method for the approximation of the fixed point of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We prove some stability and data-dependence results for this novel iterative scheme. A series of numerical illustrations and examples was constructed to validate our results. As an application, we propose a novel method for solving a certain fractional differential equation using our newly developed iterative scheme. Our results extend, unify, and improve several of the known results in the literature. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
►▼ Show Figures

Figure 1

12 pages, 221 KiB  
Article
Convergence of Infinite Products of Uniformly Locally Nonexpansive Mappings
by Simeon Reich and Alexander J. Zaslavski
Mathematics 2025, 13(5), 723; https://doi.org/10.3390/math13050723 - 24 Feb 2025
Viewed by 233
Abstract
The generic convergence of infinite products of nonexpansive mappings was established in a 1999 paper of ours. In the present paper, such results are extended to infinite products of uniformly locally nonexpansive mappings. In particular, the convergence of infinite products of uniformly locally [...] Read more.
The generic convergence of infinite products of nonexpansive mappings was established in a 1999 paper of ours. In the present paper, such results are extended to infinite products of uniformly locally nonexpansive mappings. In particular, the convergence of infinite products of uniformly locally contractive mappings, as well as its stability, are proved. Moreover, the Baire category approach and the porosity notion are used to show that most sequences of uniformly locally nonexpansive mappings are, in fact, uniformly locally contractive. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
13 pages, 215 KiB  
Article
The Krasnoselskii–Mann Method for Approximation of Coincidence Points of Set-Valued Mappings
by Alexander J. Zaslavski
Mathematics 2025, 13(4), 662; https://doi.org/10.3390/math13040662 - 18 Feb 2025
Viewed by 299
Abstract
In the present paper, we use the Krasnoselskii–Mann method in order to obtain approximate coincidence points of set-valued mappings in metric spaces with a hyperbolic structure. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
10 pages, 1880 KiB  
Article
A New Approach for Proximal Split Minimization Problems
by Abdellatif Moudafi and André Weng-Law
Mathematics 2025, 13(1), 144; https://doi.org/10.3390/math13010144 - 2 Jan 2025
Viewed by 558
Abstract
We provide an alternative formulation of proximal split minimization problems, a very recently developed and appealing strategy that relies on an infimal post-composition approach. Then, forward–backward and Douglas–Rachford splitting algorithms will guide both the design and analysis of some split numerical methods. We [...] Read more.
We provide an alternative formulation of proximal split minimization problems, a very recently developed and appealing strategy that relies on an infimal post-composition approach. Then, forward–backward and Douglas–Rachford splitting algorithms will guide both the design and analysis of some split numerical methods. We provide evidence of globally weak convergence and the fact that these algorithms can be equipped with relaxed and/or inertial steps, leading to improved convergence guarantees. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
►▼ Show Figures

Figure 1

22 pages, 764 KiB  
Article
An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings
by Habib ur Rehman, Fouzia Amir, Jehad Alzabut and Mohammad Athar Azim
Mathematics 2025, 13(1), 20; https://doi.org/10.3390/math13010020 - 25 Dec 2024
Viewed by 562
Abstract
The primary objective of this article is to enhance the convergence rate of the extragradient method through the careful selection of inertial parameters and the design of a self-adaptive stepsize scheme. We propose an improved version of the extragradient method for approximating a [...] Read more.
The primary objective of this article is to enhance the convergence rate of the extragradient method through the careful selection of inertial parameters and the design of a self-adaptive stepsize scheme. We propose an improved version of the extragradient method for approximating a common solution to pseudomonotone equilibrium and fixed-point problems that involve an infinite family of demimetric mappings in real Hilbert spaces. We establish that the iterative sequences generated by our proposed algorithms converge strongly under suitable conditions. These results substantiate the effectiveness of our approach in achieving convergence, marking a significant advancement in the extragradient method. Furthermore, we present several numerical tests to illustrate the practical efficiency of the proposed method, comparing these results with those from established methods to demonstrate the improved convergence rates and solution accuracy achieved through our approach. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Applications: 2nd Edition)
►▼ Show Figures

Figure 1

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
Cited by 1 | Viewed by 795
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 1224
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
Cited by 1 | Viewed by 1363
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)
►▼ Show Figures

Figure 1

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 712
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
Cited by 1 | Viewed by 1266
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)
►▼ Show Figures

Figure 1

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 759
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)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-11
Back to TopTop