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 andexplicit general iterative methods for a one-parameter nonexpansive semigroupin a reflexive Banach space which admits the duality mapping $J_{\phi }$, where $\phi$ is a gauge function on $\left[0,\infty \right)$. Our results improve and extend those announced by G. Marino and H.-K. Xu (2006) and many authors.