论文信息 - On the Mann iterative process

On the Mann iterative process

1. Introduction. A self-mapping F of a Banach space F is said to be nonexpansive provided \\Tx— Ty\\ ^ \\x— y\\ for all x, y e E, and is said to be quasi-nonexpansive provided that if Tp=p then \\Tx— p\\ = \\x— p\\ for all x e E (i.e., Fis nonexpansive about each of its fixed points). Nonexpansive mappings are clearly quasi-non-expansive, and linear quasi-nonexpansive mappings are nonexpansive; but it is easily seen that there exist nonlinear continuous quasi-nonexpansive mappings which are not nonexpansive, e.g. Tx = (x\2) sin (l\x), F(0) = 0, on E1. The concept of quasi-nonexpansiveness is closely related to some ideas which have been investigated recently by J. B. Diaz and F. T. Metcalf [2]. A mapping F is said to be quasi-nonexpansive on a subset C of E provided F maps C into C, and if// e C

W. G. Dotson | W. Dotson

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