Approximating fixed points of non-self nonexpansive mappings in Banach spaces

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K -> E be a nonexpansive non-self map with F(T) : = {x is an element of K : Tx = x) not equal 0. Suppose [x,(n)} is generated iteratively by [Graphics] n >= 1, where {alpha(n)} and {beta(n)} are real sequences in [epsilon, 1-epsilon] for some epsilon is an element of (0, 1). (1) If the dual E* of E has the Kadec-Klee property, then weak convergence of {x(n)} to some x* is an element of F(T) is proved; (2) If T satisfies condition (A), then strong convergence of {x(n)} to some x* is an element of F(T) is obtained. (c) 2005 Elsevier Ltd. All rights reserved.