Strong convergence of viscosity iterations with error terms for cosine families in Banach spaces

Abstract

In this paper viscosity iterations with error terms for approximating common fixed points of a nonexpansive cosine family and a continuous pseudocontractions are firstly considered. By using the theory of cosine families and constructing some control conditions, several new strong convergence results for this iterative process are presented in the bounded subsets of real uniformly convex and uniformly Gâteaux differentiable Banach spaces, and in the unnecessarily bounded subsets of real reflexive Banach spaces which admit a weakly sequentially continuous duality mapping, respectively. The results contain the corresponding ones without errors as their special cases.