J. Korean Math. Soc. 2003; 40(1): 29-40
Printed January 1, 2003
Copyright © The Korean Mathematical Society.
Z. Liu, S. M. Kang, and S. H. Shim
Liaoning Normal University, Gyeongsang National University, Gyeongsang National University
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
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd