Convergence Theorems for Equilibrium Problems and Fixed‐Point Problems of an Infinite Family of k_i‐Strictly Pseudocontractive Mapping in Hilbert Spaces

Abstract

We first extend the definition of Wnfrom an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family ofki-strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.