A new general iterative methods for solving the equilibrium problems, variational inequality problems and xed point problems of nonexpansive mappings

Ekkarath Thailert, R. Wangkeeree, Pakkapon Preechasilp

Abstract

In this paper, we introduce the new general iterative methods for nding a common solutionset of equilibrium problems and the set of xed points of nonexpansive mappings which isa solution of a certain optimization problem related to a strongly positive linear operator.Under suitable control conditions, we prove the strong convergence theorems of such iterativescheme in a real Hilbert space. The main result extends various results existing in the currentliterature.