Journal of the
Korean Mathematical Society
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ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2003; 40(1): 29-40

Printed January 1, 2003

Copyright © The Korean Mathematical Society.

Almost stability of the Mann iteration method with errors for strictly hemi-contractive operators in Smooth Banach spaces

Z. Liu, S. M. Kang, and S. H. Shim

Liaoning Normal University, Gyeongsang National University, Gyeongsang National University

Abstract

Let $K$ be a nonempty closed bounded convex subset of an arbitrary smooth Banach space $X$ and $T:K\to K$ be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of $T$ and is almost $T$-stable on $K$. The results presented in this paper generalize the corresponding results in [1]-[7], [20] and others.

Keywords: Mann iteration method with errors, strictly hemi-contactive operators, strongly pseudocontractive operators, local strongly pseudocontractive operators, smooth Banach spaces

MSC numbers: 47H06, 47H10, 47H15, 47H17

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