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 Frechet differentiable norm. Let A : D(A) subset of 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 alpha-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 is an element of Sx + lambdaAx for given z is an element of X and lambda > 0. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 36]