Existence and Algorithm for Generalized Mixed Equilibrium Problem with a Relaxed Monotone Mapping

Prapairat Junlouchai, Somyot Plubtieng

Abstract

In this paper, we introduce a new generalized mixed equilibrium problem with a relaxed monotone mapping.By using KKM theorem, we establish an existence theorem for this problem in a Hausdorff topological vector space.Moreover, we introduce an iterative sequence and prove a weak convergence theorem for a generalized mixed equilibriumproblem with a relaxed monotone mapping in Hilbert spaces. The results presented in this paper can be viewed asgeneralization and extension of many results in literature.