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Strong convergence theorems for fixed points of pseudo-contractive semigroup

Published online by Cambridge University Press:  17 April 2009

Xue-Song Li  and
Nan-Jing Huang
Xue-Song Li
Affiliation:
Department of Mathematics, Sichuan University, Chengdu Sichuan, 610064, People's Republic of China, e-mail: xuesongli78@hotmail.comnanjinghuang@hotmail.com
Nan-Jing Huang
Affiliation:
Department of Mathematics, Sichuan University, Chengdu Sichuan, 610064, People's Republic of China, e-mail: xuesongli78@hotmail.comnanjinghuang@hotmail.com
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Abstract

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We study some convergence of two kinds of implicit iteration processes for approximating common fixed points of a pseudo-contractive semigroup in uniformly convex Banach spaces with uniformly Gateaux differential norms. As special cases, we get some convergence of the implicit iteration processes for approximating common fixed points of a nonexpansive semigroup in uniformly smooth Banach spaces and give a positive answer to an open problem proposed by Xu in Bull. Austral. Math. Soc. (2005). The results presented in this paper generalise some corresponding results from Osilike in Panamer. Math. J. (2004), Suzuki in Proc. Amer. Math. Soc. (2002) and Xu in Bull. Austral. Math. Soc. (2005).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 3 , December 2007 , pp. 441 - 452
Copyright
Copyright © Australian Mathematical Society 1999

References

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