Open Access Research

Strong convergence for asymptotical pseudocontractions with the demiclosedness principle in banach spaces

Yuan-Heng Wang* and Yong-Hui Xia

Author Affiliations

Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, China

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Fixed Point Theory and Applications 2012, 2012:45  doi:10.1186/1687-1812-2012-45

Published: 23 March 2012

Abstract

The aim of this article is to give an answer to an interesting question proposed in Zhou. At the end of his article, he remarked that it was of great interest to extend his results to certain Banach spaces. So in this article, we extend the demiclosedness principle from Hilbert spaces to Banach spaces. A strong convergence theorem for asymptotical pseudo-contractions in Banach spaces is established. The approaches are based on the extended demiclosedness principle, and the generalized projective operator, and the hybrid method in mathematical programming. Our results extend the previous known results from Hilbert spaces to Banach spaces.

MSC: 47H10; 47H09; 47H05.

Keywords:
demiclosedness principle; generalized projection; strong convergence; asymptotically pseudo-contractions; Banach space