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 W_n from 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 of $k_i$-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.