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.