Abstract
Let K be a nonempty closed convex subset of a real reflexive Banach space E that has weakly continuous duality mapping J(phi) for some gaugeo phi. Let T-i : K -> K, i = 1, 2,..., be a family of quasi-nonexpansive mappings with F := boolean AND(i >= 1>) F(T-i) not equal empty set which is a sunny nonexpansive retract of K with Q a nonexpansive retraction. For given x(0) epsilon K, let {x(n)} be generated by the algorithm Xn+1 := alpha(n) f(x(n)) + (1 - alpha(n))T-n(x(n)), n >= 0, where f : K -> K is a contraction mapping and {alpha(n)} subset of (0, 1) a sequence satisfying certain conditions. Suppose that {x(n)} satisfies condition (A). Then it is proved that {x(n)} converges strongly to a common fixed point (x) over bar = Qf ((x) over bar) of a family T-i, i = 1, 2,... Moreover, is the unique solution in F to a certain variational inequality. (c) 2007 Elsevier Ltd. All rights reserved.