Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping, the set of solutions of the variational inequality for the monotone mapping and the set of solutions of an equilibrium problem in a 2-uniformly convex and uniformly smooth Banach space. Then we show that the iterative sequence converges strongly to a common element of the three sets. In this paper, we also give an example which is a weak relatively nonexpansive mapping but not a relatively nonexpansive mapping in Banach space l 2 .