## Abstract and Applied Analysis

### Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

#### 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).

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 297565, 16 pages.

Dates
First available in Project Euclid: 16 March 2010

https://projecteuclid.org/euclid.aaa/1268745620

Digital Object Identifier
doi:10.1155/2009/297565

Mathematical Reviews number (MathSciNet)
MR2576579

Zentralblatt MATH identifier
1195.47042

#### Citation

Cholamjiak, Watcharaporn; Suantai, Suthep. Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings. Abstr. Appl. Anal. 2009 (2009), Article ID 297565, 16 pages. doi:10.1155/2009/297565. https://projecteuclid.org/euclid.aaa/1268745620

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