Special Issue "Applied Functional Analysis and Its Applications"

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

Deadline for manuscript submissions: closed (31 March 2020).

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Jen-Chih Yao
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
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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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 (11 papers)

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Research

Open AccessArticle
A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing
Mathematics 2020, 8(2), 288; https://doi.org/10.3390/math8020288 - 20 Feb 2020
Cited by 2 | Viewed by 498
Abstract
In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments [...] Read more.
In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms. Full article
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Open AccessArticle
Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems
Mathematics 2020, 8(2), 236; https://doi.org/10.3390/math8020236 - 12 Feb 2020
Cited by 4 | Viewed by 609
Abstract
In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied [...] Read more.
In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field. Full article
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Open AccessArticle
An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces
Mathematics 2020, 8(1), 143; https://doi.org/10.3390/math8010143 - 20 Jan 2020
Viewed by 759
Abstract
This paper explores new notions of approximate minimality in set optimization using a set approach. We propose characterizations of several approximate minimal elements of families of sets in real linear spaces by means of general functionals, which can be unified in an inequality [...] Read more.
This paper explores new notions of approximate minimality in set optimization using a set approach. We propose characterizations of several approximate minimal elements of families of sets in real linear spaces by means of general functionals, which can be unified in an inequality approach. As particular cases, we investigate the use of the prominent Tammer–Weidner nonlinear scalarizing functionals, without assuming any topology, in our context. We also derive numerical methods to obtain approximate minimal elements of families of finitely many sets by means of our obtained results. Full article
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Open AccessArticle
Convergence Theorems for Modified Implicit Iterative Methods with Perturbation for Pseudocontractive Mappings
Mathematics 2020, 8(1), 72; https://doi.org/10.3390/math8010072 - 02 Jan 2020
Viewed by 462
Abstract
In this paper, first, we introduce a path for a convex combination of a pseudocontractive type of mappings with a perturbed mapping and prove strong convergence of the proposed path in a real reflexive Banach space having a weakly continuous duality mapping. Second, [...] Read more.
In this paper, first, we introduce a path for a convex combination of a pseudocontractive type of mappings with a perturbed mapping and prove strong convergence of the proposed path in a real reflexive Banach space having a weakly continuous duality mapping. Second, we propose two modified implicit iterative methods with a perturbed mapping for a continuous pseudocontractive mapping in the same Banach space. Strong convergence theorems for the proposed iterative methods are established. The results in this paper substantially develop and complement the previous well-known results in this area. Full article
Open AccessArticle
Informal Norm in Hyperspace and Its Topological Structure
Mathematics 2019, 7(10), 945; https://doi.org/10.3390/math7100945 - 11 Oct 2019
Viewed by 533
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
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
Cited by 5 | Viewed by 828
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
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
Cited by 5 | Viewed by 754
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
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
Cited by 10 | Viewed by 772
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
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
Viewed by 661
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
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
Viewed by 607
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
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
Viewed by 674
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
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