부산대학교 도서관

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∥≤( 17/18 )n+1∥x0 - q∥ where q ∈ X is a solution of x + AX = f . [ABSTRACT FROM AUTHOR]