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J. Korean Math. Soc. 1998; 35(1): 191-205

Printed March 1, 1998

Copyright © The Korean Mathematical Society.

Iterative process with errors for $m$-accretive operators

J. H. Baek, Y. J. Cho, and S. S. Chang

Gyeongsang National University, Gyeongsang National University and Sichuan University

Abstract

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In this paper, we prove that the Mann and Ishikawa iteration sequences with errors converge strongly to the unique solution of the equation $x+Tx=f$, where $T$ is an $\text{\it m}$-accretive operator in uniformly smooth Banach spaces. Our results extend and improve those of Chidume, Ding, Zhu and others.

Keywords: m-accretive operator, the Mann and Ishikawa iteration sequences with errors

MSC numbers: 47H17, 47H06, 47H10

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