VARIATIONAL RELATION PROBLEMS IN ABSTRACT CONVEX SPACES (Study on Nonlinear Analysis and Convex Analysis)

Abstract

In 2008, Luc initiated the study of variational relations, which is a unifying approach to various models of equilibrium theory and variational inclusions. In 2018, we generalized some of Luc's results by reflecting recent development of the KKM theory on abstract convex spaces. Moreover in 2019, we obtain some abstract space versions of known results on generalized KKM maps and variational relation problems appeared in the papers of Park and Lee; Balaj and Luc; Luc, Sarabi and Soubeyran; Lin; and Balaj, in the chronological order. In this talk, we introduce some contents of our papers in 2018 and 2019.