Applications of the KKM Property to Coincidence Theorems, Equilibrium Problems, Minimax Inequalities and Variational Relation Problems. (3rd April 2017)

• Record Type: Journal Article
• Authors: Patriche, Monica
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 4(2017)
• Page Start: 523
• Page End: 548
• Publication Date: 2017-04-03
• Subjects: Coincidence theorem -- equilibrium problem -- KKM property -- minimax inequality -- variational relation problem; 49J35 -- 91B50; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1287085
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. To do this, we define new type of correspondences, namely, properly quasi-convex-like correspondences. Further, we apply the obtained theorems to solve equilibrium problems and to establish a minimax inequality. In the last part of the paper, we study the existence of solutions for generalized vector variational relation problems. Our analysis is based on the applications of the KKM principle. We establish existence theorems involving new hypothesis and we improve the results of some recent papers.