A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

Abstract

We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping Jφ, where φ is a gauge function on [0,∞). Our results improve and extend those announced by G. Marino and H.-K. Xu (2006) and many authors.