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

AbstractLet E be an arbitrary real Banach space and T:E→E be a Lipschitz continuous accretive operator. Under the lack of the assumption limn→∞αn=limn→∞βn=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