Existence Theorems for a Variational Relation Problem. (2nd April 2016)

• Record Type: Journal Article
• Authors: Balaj, Mircea
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 4(2016)
• Page Start: 459
• Page End: 479
• Publication Date: 2016-04-02
• Subjects: Fixed point -- quasivariational inclusion -- set-valued mapping -- variational relation problem; 49J40 -- 49J53; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1136327
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The aim of this article is to establish new existence results for a certain type of variational relation problem studied by Agarwal et al. in a very recent article. This problem is a general model for several quasivariational inclusions and quasiequilibrium problems investigated in many recent articles. The main tools in proving the existence theorems are two well-known fixed point theorems (Eilenberg-Montgomery and Kakutany-Fan Glicksberg, respectively). In the last section, we prove that, applied in special cases, our results are different or stronger than several earlier results.