The viscosity approximation method for accretive operators in Banach spaces

Abstract

We extend the viscosity approximation method (VAM) to accretive operators (via their resolvents) in a uniformly convex and/or uniformly Gâteaux differentiable Banach space X to find a zero of an m-accretive operator and of the sum of two m-accretive operators. In all cases, we prove the strong convergence of our VAM algorithms and the limit of the iterates is identified as the unique sunny nonexpansive retraction onto to the zero set of the operator.