Iterative methods with mixed errors for perturbed m-accretive operator equations in arbitrary Banach spaces

Abstract

Let X be a real Banach space, A : X → 2 X a uniformly continuous m-accretive operator with nonempty closed values and bounded range R( A), and S : X → X a uniformly continuous strongly accretive operator with bounded range R( I – S). It is proved that the Ishikawa and Mann iterative processes with mixed errors converge strongly to unique solution of the equation z ϵ Sx + λ Ax for given z ϵ X and λ > 0. As an immediate consequence, in case that λ = 0 and S : X → 2 X is uniformly continuous strongly accretive, some convergence theorems of Ishikawa and Mann type iterative processes with mixed errors for approximating unique solution of the equation z ϵ Sx are also obtained.