Lexicographical operator equilibrium problems

Abstract

In this paper, we introduced and studied lexicographical operator equilibrium problem by using lexicographical cone in R². Also, we prove an existence result for solution of this problem by using Kakutani fixed point theorem. As corollaries existence results for lexicographical operator variational inequalities and lexicographical operator minimization problems are also discussed. Our results in this paper are new which can be considered as significant extension of previously known results in the literature.