Iterative approximation of solutions to nonlinear equations involving m-accretive operators in Banach spaces

摘要

Let E be an arbitrary real Banach space and T: E --> E be a Lipschitz continuous accretive operator. Under the lack of the assumption lim(n-->infinity) alpha(n) lim(n-->infinity) beta(n) = 0, we prove that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation x + Tx = f. Moreover, this result provides a convergence rate estimate for some special cases of such a sequence. Utilizing this result, we imply that if T : E --> E is a Lipschitz continuous strongly accretive operator then the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation Tx = f. Our results improve, generalize and unify the ones of Liu, Chidume and Osilike, and to some extent, of Reich. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 20]