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Let X be a Banach space. Suppose that A:X→X is a Lipschitz accretive operator. The objective of this note is to discuss simultaneously the existence and uniqueness of solution of the equation x+Ax=f for any given f∈X, and its convergence, estimate of convergent rate, and stability of Krasnosel’skiĭ-Mann-Opial type iterative solution {xn}⊆X. 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 ∥xn+1−q∥≤(1718)n+1∥x0−q∥ where q∈X is a solution of x+AX=f.

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