New Iterative Scheme for an Infinite Family of Nonexpansive Maps

摘要

In 2006,Chang proved that the sequence {xn} generated by the iteration xn+1=bn+1 f(Xn) + (1-bn+1)Tn+1Xn converges strongly to a common fixed point of a finite family of nonexpansive mappings {Tn} in uniformly smooth Banach spaces, where f is a contraction self-mapping. In this paper, the author considers the iteration in more general case that {Tn} is an infinite family of nonexpansive mappings, and proves that Chang's result holds still in the framework of reflexive Banach spaces with the weakly sequentially continuous duality mapping.