Iterative processes with mixed errors for nonlinear equations with perturbed m-accretive operators in Banach spaces

Abstract

Let X be a real uniformly smooth Banach space of which the dual X ∗ has a Fréchet differentiable norm. Let A: D( A)⊂ X→2 X be an m-accretive operator with closed domain D( A) and bounded range R( A) and S: X→ X a continuous and α-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 the unique solution of the equation z∈ Sx+ λAx for given z∈ X and λ>0.