The Applications of Modified Generalized Mixed Equilibrium Problems to Nonlinear Problems

Wongvisarut Khuangsatung, Atid Kangtunyakarn

Abstract

From the concept of generalized mixed equilibrium  problems, we introduce a new problem to  prove a strong convergence theorem for finding a common element of the set of fixed point of an infinite family of  nonexpansive mappings and the set of a finite family of generalized mixed equilibrium  problems in Hilbert space. We also apply our main result for  generalized  equilibrium  problems and  variational inequalities problems.