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

摘要

Let X be a real uniformly smooth Banach space of which the dual X∗ has a Fréchet differentiable norm. Let A:D(A)⊂X→2X 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.