Approximating fixed points of nonexpansive mappings

Abstract

We consider a mapping S of the form urn:x-wiley:01611712:media:ijmm542948:ijmm542948-math-0001 , where α i ≥ 0, α 0 > 0, α 1 > 0 and . We show that the Picard iterates of S converge to a common fixed point of T i ( i = 1,2,…, k )in a Banach space when T i ( i = 1,2,…, k ) are nonexpansive.