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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 912545, 11 pages
http://dx.doi.org/10.1155/2012/912545
Research Article

Strong Convergence Theorems for Modifying Halpern Iterations for Quasi- -Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications

School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China

Received 20 August 2012; Accepted 21 November 2012

Academic Editor: Nan-Jing Huang

Copyright © 2012 Li Yi. 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

An iterative sequence for quasi- -asymptotically nonexpansive multivalued mapping for modifying Halpern's iterations is introduced. Under suitable conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results in the work by Chang et al. 2011.