Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type

Abstract

In this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem, set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which are announced recently. Application of our theorem to solution of equations of Hammerstein-type is of independent interest.