The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>φ</mml:mi></mml:math>-strongly accretive operators in uniformly smooth Banach spaces

Liu, Zeqing; Wang, Li; Ume, Jeong Sheok; Kang, Shin Min

doi:https://doi.org/10.1155/IJMMS/2006/69542

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 069542 | https://doi.org/10.1155/IJMMS/2006/69542

The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces

Zeqing Liu,¹Li Wang,²Jeong Sheok Ume,³and Shin Min Kang⁴

Received22 Oct 2004

Revised05 Mar 2006

Accepted12 Mar 2006

Published24 May 2006

Abstract

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for φ-pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve the corresponding results in the literature.

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Copyright © 2006 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.

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