Iterative approaches to convex feasibility problems in Banach spaces

The convex feasibility problem (CFP) of finding a point in the nonempty intersection boolean AND(N)(i=1) C-i is considered, where N >= 1 is an integer and each C-i is assumed to be the fixed point set of a nonexpansive mapping T-i : X -> X with X a Banach space. It is shown that the iterative scheme x(n+1) = lambda(n+1)y + (1 - lambda(n+1))T(n+1)x(n) is strongly convergent to a solution of (CFP) provided the Banach space X either is uniformly smooth or is reflexive and has a weakly continuous duality map, and provided the sequence {lambda(n)} satisfies certain conditions. The limit of {x(n)} is located as Q(y), where Q is the sunny nonexpansive retraction from X onto the common fixed point set of the T-i'S. (c) 2005 Elsevier Ltd. All rights reserved.