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2009 Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
Watcharaporn Cholamjiak, Suthep Suantai
Abstr. Appl. Anal. 2009: 1-16 (2009). DOI: 10.1155/2009/297565

Abstract

We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).

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Watcharaporn Cholamjiak. Suthep Suantai. "Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings." Abstr. Appl. Anal. 2009 1 - 16, 2009. https://doi.org/10.1155/2009/297565

Information

Published: 2009
First available in Project Euclid: 16 March 2010

zbMATH: 1195.47042
MathSciNet: MR2576579
Digital Object Identifier: 10.1155/2009/297565

Rights: Copyright © 2009 Hindawi

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