GENERALIZED PROJECTION AND ITERATIVE METHODS FOR APPROXIMATING FIXED POINTS OF ASYMPTOTICALLY WEAKLY SUPPRESSIVE OPERATORS

Abstract

Let $C$ be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space $E$, let $S: C \to C$ be a relatively nonexpansive mapping, and let $T: C \to E$ be an asymptotically weakly suppressive operator. Using the notion of generalized projection, iterative methods for approximating common fixed points of the mappings $S$ and $T$ are studied. In terms of the modified Ishikawa iteration and modified Halpern one for relatively nonexpansive mappings, we propose two modified versions of Chidume, Khumalo and Zegeye's iterative algorithms [C.E. Chidume, M. Khumalo and H. Zegeye, Generalized projection and approximation of fixed points of nonself maps, J. Appro. Theory, 120 (2003) 242-252] for finding approximate common fixed points of the mappings $S$ and $T$. Moreover, it is proved that these two iterative algorithms converge strongly to the same common fixed point of the mappings $S$ and $T$.