Special Issue "Applied Functional Analysis and Its Applications"

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

Deadline for manuscript submissions: 31 October 2019.

Special Issue Editors

Prof. Dr. Jen-Chih Yao
E-Mail Website
Guest Editor
Research Center for Interneural Computing, China Medical University Hospital, China Medical University,Taichung, Taiwan
Interests: vector optimization; fixed point theory; variational inequalities; complementarity problems; variational analysis; equilibrium problems; optimal control; generalized convexity and generalized monotonicity
Prof. Dr. Shahram Shahram Rezapour
E-Mail Website
Guest Editor
1. Department of Medical Research, China Medical University, Taiwan
2. Department of Mathematics, Azerbaijan Shahid Madani University, Tabriz, Iran
Interests: approximation theory; fixed point theory; fractional differential equations; fractional finite difference equations
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

It is very well known that applied functional analysis is very important in most applied research fields, and its influence has grown in recent decades. It seems that most novel papers have used techniques, idea, notions, and methods of applied functional analysis. As you know, applied functional analysis incudes linear and nonlinear problems. This Special Issue deals mainly with the theoretical approaches to such problems; in particular, any work including new ideas, novelty techniques, and/or results on applied functional analysis are welcome. We accept high-quality research or review papers. The purpose of this Special Issue is to connect the efforts of various scientists (particularly mathematicians and engineers) for whom applied functional analysis is important in their research activity.

Prof. Dr. Jen-Chih Yao
Prof. Dr. Shahram Rezapour
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 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 1200 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

  • Functional analysis
  • Fixed point theory
  • Fractional integro-differential equations and inclusions
  • Linear and nonlinear problems
  • Optimization theory
  • Applications of functional analysis
  • Variational inequalities
  • Complementarity problems
  • Variational analysis
  • Numerical optimization.

Published Papers (7 papers)

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Research

Open AccessArticle
Informal Norm in Hyperspace and Its Topological Structure
Mathematics 2019, 7(10), 945; https://doi.org/10.3390/math7100945 - 11 Oct 2019
Abstract
The hyperspace consists of all subsets of a vector space. Owing to a lack of additive inverse elements, the hyperspace cannot form a vector space. In this paper, we shall consider a so-called informal norm to the hyperspace in which the axioms regarding [...] Read more.
The hyperspace consists of all subsets of a vector space. Owing to a lack of additive inverse elements, the hyperspace cannot form a vector space. In this paper, we shall consider a so-called informal norm to the hyperspace in which the axioms regarding the informal norm are almost the same as the axioms of the conventional norm. Under this consideration, we shall propose two different concepts of open balls. Based on the open balls, we shall also propose the different types of open sets. In this case, the topologies generated by these different concepts of open sets are investigated. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
Open AccessFeature PaperArticle
On Mann Viscosity Subgradient Extragradient Algorithms for Fixed Point Problems of Finitely Many Strict Pseudocontractions and Variational Inequalities
Mathematics 2019, 7(10), 925; https://doi.org/10.3390/math7100925 - 04 Oct 2019
Abstract
In a real Hilbert space, we denote CFPP and VIP as common fixed point problem of finitely many strict pseudocontractions and a variational inequality problem for Lipschitzian, pseudomonotone operator, respectively. This paper is devoted to explore how to find a common solution of [...] Read more.
In a real Hilbert space, we denote CFPP and VIP as common fixed point problem of finitely many strict pseudocontractions and a variational inequality problem for Lipschitzian, pseudomonotone operator, respectively. This paper is devoted to explore how to find a common solution of the CFPP and VIP. To this end, we propose Mann viscosity algorithms with line-search process by virtue of subgradient extragradient techniques. The designed algorithms fully assimilate Mann approximation approach, viscosity iteration algorithm and inertial subgradient extragradient technique with line-search process. Under suitable assumptions, it is proven that the sequences generated by the designed algorithms converge strongly to a common solution of the CFPP and VIP, which is the unique solution to a hierarchical variational inequality (HVI). Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
Open AccessFeature PaperArticle
Inertial-Like Subgradient Extragradient Methods for Variational Inequalities and Fixed Points of Asymptotically Nonexpansive and Strictly Pseudocontractive Mappings
Mathematics 2019, 7(9), 860; https://doi.org/10.3390/math7090860 - 17 Sep 2019
Abstract
Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish [...] Read more.
Let VIP indicate the variational inequality problem with Lipschitzian and pseudomonotone operator and let CFPP denote the common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space. Our object in this article is to establish strong convergence results for solving the VIP and CFPP by utilizing an inertial-like gradient-like extragradient method with line-search process. Via suitable assumptions, it is shown that the sequences generated by such a method converge strongly to a common solution of the VIP and CFPP, which also solves a hierarchical variational inequality (HVI). Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
Open AccessArticle
A Solution for Volterra Fractional Integral Equations by Hybrid Contractions
Mathematics 2019, 7(8), 694; https://doi.org/10.3390/math7080694 - 01 Aug 2019
Abstract
In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and [...] Read more.
In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
Open AccessArticle
Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications
Mathematics 2019, 7(6), 517; https://doi.org/10.3390/math7060517 - 06 Jun 2019
Abstract
In this paper, we are concerned with the ψ-fractional integrals, which is a generalization of the well-known Riemann–Liouville fractional integrals and the Hadamard fractional integrals, and are useful in the study of various fractional integral equations, fractional differential equations, and fractional integrodifferential [...] Read more.
In this paper, we are concerned with the ψ-fractional integrals, which is a generalization of the well-known Riemann–Liouville fractional integrals and the Hadamard fractional integrals, and are useful in the study of various fractional integral equations, fractional differential equations, and fractional integrodifferential equations. Our main goal is to present some new properties for ψ-fractional integrals involving a general function ψ by establishing several new equalities for the ψ-fractional integrals. We also give two applications of our new equalities. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
Open AccessArticle
A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems
Mathematics 2019, 7(4), 372; https://doi.org/10.3390/math7040372 - 24 Apr 2019
Abstract
In this paper, we introduce the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative. Then by virtue of the epiderivative and Benson proper efficiency, we establish the [...] Read more.
In this paper, we introduce the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative. Then by virtue of the epiderivative and Benson proper efficiency, we establish the higher-order Mond-Weir type dual problem for a set-valued optimization problem and obtain the corresponding weak duality, strong duality and converse duality theorems, respectively. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
Open AccessArticle
Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces
Mathematics 2019, 7(4), 345; https://doi.org/10.3390/math7040345 - 10 Apr 2019
Abstract
The aim of this article is to study new types of generalized nonsmooth exponential type vector variational-like inequality problems involving Mordukhovich limiting subdifferential operator. We establish some relationships between generalized nonsmooth exponential type vector variational-like inequality problems and vector optimization problems under some [...] Read more.
The aim of this article is to study new types of generalized nonsmooth exponential type vector variational-like inequality problems involving Mordukhovich limiting subdifferential operator. We establish some relationships between generalized nonsmooth exponential type vector variational-like inequality problems and vector optimization problems under some invexity assumptions. The celebrated Fan-KKM theorem is used to obtain the existence of solution of generalized nonsmooth exponential-type vector variational like inequality problems. In support of our main result, some examples are given. Our results presented in this article improve, extend, and generalize some known results offer in the literature. Full article
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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