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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 623625, 7 pages
doi:10.1155/2012/623625
Fixed Point of Strong Duality Pseudocontractive Mappings and Applications
Department of Mathematics, Cangzhou Normal University, Cangzhou 061001, China
Received 16 July 2012; Accepted 22 July 2012
Academic Editor: Yongfu Su
Copyright © 2012 Baowei Liu. 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
Let E be a smooth Banach space with the dual , an operator is said to be α-strong duality pseudocontractive if , for all , where α is a nonnegative constant. An element is called a duality fixed point of T if . The purpose of this paper is to introduce the definition of α-strong duality pseudocontractive mappings and to study its fixed point problem and applications for operator equation and variational inequality problems.