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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 207896, 9 pages
Research Article

New Iterative Manner Involving Sunny Nonexpansive Retractions for Pseudocontractive Mappings

1College of Science, Agricultural University of Hebei, Baoding 071001, China
2North China Electric Power University, Baoding 071003, China

Received 19 September 2012; Accepted 8 October 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Yaqin Zheng and Jinwei Shi. 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.


Iterative methods for pseudocontractions have been studied by many authors in the literature. In the present paper, we firstly propose a new iterative method involving sunny nonexpansive retractions for pseudocontractions in Banach spaces. Consequently, we show that the suggested algorithm converges strongly to a fixed point of the pseudocontractive mapping which also solves some variational inequality.