Special Issue "Variational Inequality"

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

Deadline for manuscript submissions: 31 December 2019

Special Issue Editor

Guest Editor
Prof. Dr. Jen-Chih Yao

Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taiwan
Website | E-Mail
Interests: vector optimization; fixed point theory; variational inequalities; complementarity problems; variational analysis; equilibrium problems; optimal control; generalized convexity and generalized monotonicity

Special Issue Information

Dear Colleagues,

It is well known that variational inequality was introduced by Hartman and Stampacchia in 1966, and was later expanded by Stampacchia. Since then, variational inequality and its various generalizations have become very effective and quite powerful tools in the study of the many problems arising from differential equations, mechanics, contact problems, optimization and control problems, management science, operations research, general equilibrium problems in economics and transportation, unilateral, obstacle, moving, and so on. The motivation of this Special Issue is to report and collect the recent developments of variational inequality in both theory and applications. This Special Issue deals mainly with the theory and applications of variational inequalities and related problems; in particular, any work including new ideas, novelty techniques, and/or results on variational inequalities and its relevant problems are welcome. We are accepting 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 various variational inequality problems are important in their research activity.

Prof. Dr. Jen-Chih Yao
Guest Editor

Manuscript Submission Information

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Keywords

  • Variational inequality
  • Complementarity problem
  • Variational analysis
  • Optimization
  • Optimal control

Published Papers (3 papers)

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Research

Open AccessArticle
Strong Convergence Theorems for Variational Inequalities and Common Fixed-Point Problems Using Relaxed Mann Implicit Iteration Methods
Mathematics 2019, 7(5), 424; https://doi.org/10.3390/math7050424
Received: 10 March 2019 / Revised: 6 May 2019 / Accepted: 7 May 2019 / Published: 11 May 2019
PDF Full-text (271 KB)
Abstract
Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a [...] Read more.
Mann-like iteration methods are significant to deal with convex feasibility problems in Banach spaces. We focus on a relaxed Mann implicit iteration method to solve a general system of accretive variational inequalities with an asymptotically nonexpansive mapping in the intermediate sense and a countable family of uniformly Lipschitzian pseudocontractive mappings. More convergence theorems are proved under some suitable weak condition in both 2-uniformly smooth and uniformly convex Banach spaces. Full article
(This article belongs to the Special Issue Variational Inequality)
Open AccessArticle
Generalized Implicit Set-Valued Variational Inclusion Problem with ⊕ Operation
Mathematics 2019, 7(5), 421; https://doi.org/10.3390/math7050421
Received: 6 March 2019 / Revised: 7 May 2019 / Accepted: 8 May 2019 / Published: 10 May 2019
PDF Full-text (245 KB)
Abstract
In this paper, we consider a resolvent operator which depends on the composition of two mappings with ⊕ operation. We prove some of the properties of the resolvent operator, that is, that it is single-valued as well as Lipschitz-type-continuous. An existence and convergence [...] Read more.
In this paper, we consider a resolvent operator which depends on the composition of two mappings with ⊕ operation. We prove some of the properties of the resolvent operator, that is, that it is single-valued as well as Lipschitz-type-continuous. An existence and convergence result is proven for a generalized implicit set-valued variational inclusion problem with ⊕ operation. Some special cases of a generalized implicit set-valued variational inclusion problem with ⊕ operation are discussed. An example is constructed to illustrate some of the concepts used in this paper. Full article
(This article belongs to the Special Issue Variational Inequality)
Open AccessArticle
Systems of Variational Inequalities with Nonlinear Operators
Mathematics 2019, 7(4), 338; https://doi.org/10.3390/math7040338
Received: 2 March 2019 / Revised: 2 April 2019 / Accepted: 3 April 2019 / Published: 9 April 2019
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Abstract
In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly [...] Read more.
In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces. Full article
(This article belongs to the Special Issue Variational Inequality)
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