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 [1,7,9].