Viscosity approximation methods for pseudo-contractive semigroups in Banach spaces

Abstract

We study the strong convergence of two viscosity iteration processes for pseudo-contractive semigroup and for ϕ-strongly pseudo-contractive mapping in uniformly convex Banach spaces with uniformly Gâteaux differentiable norm. As special cases, we get strong convergence of two viscosity iteration processes for approximating common fixed points of nonexpansive semigroups in certain Banach spaces. The results presented in this paper extend and generalize previous results.