Strong Convergence of the Modified Mann Iterations in a Banach Space

S. Imnang, S. Suantai

Abstract

The Mann iterations for nonexpansive mappings have only weak convergence even in a Hilbert space. We propose two modifications of the Mann iterations in a uniformly smooth Banach space, one for nonexpansive mappings and the other for the resolvent of accretive operators. The two modified Mann iterations are proved to have strong convergence.