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International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 10, Pages 611-617
http://dx.doi.org/10.1155/S0161171202112257

Convergence theorems and stability results for Lipschitz strongly pseudocontractive operators

Zeqing Liu,1 Lili Zhang,1 and Shin Min Kang2

1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Liaoning, Dalian 116029, China
2Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

Received 17 December 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Suppose that X is an arbitrary real Banach space and T:X→X is a Lipschitz strongly pseudocontractive operator. It is proved that under certain conditions the Ishikawa iterative method with errors converges strongly to the fixed point of T and this iteration procedure is stable with respect to T.