Strong convergence of an iterative scheme for accretive operators in Banach spaces

Abstract

In 2009, Kumam [7] introduced a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for monotone, Lipschitz-continuous mappings and proved its strong convergence in a real Hilbert space. The aim of this paper is to prove a strong convergence result of this iterative scheme in the setting of Banach spaces involving an inverse strongly accretive operator under some conditions. As a special case, we shall prove that proposed iterative scheme converges strongly to minimum norm solution of some variational inequality problem.