Existence of solutions for a new version of generalized operator equilibrium problems

Abstract

In this paper, a system of generalized operator equilibrium problems(for short, SGOEP) in the setting of topological vector spaces is introduced. Applying some properties of the nonlinear scalarization mapping and the maximal element lemma an existence theorem for SGOEP is proved. Moreover, using Ky Fan's lemma an existence result for the generalized operator equilibrium problem(for short, GOEP) is established. The results of the paper can be viewed as a generalization and improvement of the corresponding results given in [1, 2, 5, 8].