Krasnosel’skiĭ-Mann-Opial type iterative solution of m -accretive operator equation and its stability in arbitrary Banach spaces

Let X be a Banach space. Suppose that is a Lipschitz accretive operator. The objective of this note is to discuss simultaneously the existence and uniqueness of solution of the equation for any given , and its convergence, estimate of convergent rate, and stability of Krasnosel’skiĭ-Mann-Opial type iterative solution . If an iterative parameter is selected suitably then the iterative procedure converges strongly to a unique solution of the equation and the iterative process is stable in arbitrary Banach space without any convexity or reflexivity. In particular, if A is nonexpansive then an estimate of the convergence rate can be written as where is a solution of . MSC: 47H06, 47H10, 47H17.