The modification of generalized mixed equilibrium problems for convergence theorem of variational inequality problems and fixed point problems

Abstract

The purpose of this research, we modify generalized mixed equilibrium problems and prove a strong convergence theorem for approximating a common element of the set of such a problem and variational inequality problems and the set of fixed points of infinite family of strictly pseudo contractive mappings. Utilizing our main result, we also prove a strong convergence theorem involving generalized equilibrium problems and variational inequality problems.