Fixed Point of Strong Duality Pseudocontractive Mappings and Applications

Let E be a smooth Banach space with the dual E*, an operator T : E -> E* is said to be alpha-strong duality pseudocontractive if < x - y, Tx - Ty > <= < x - y, Jx - Jy > - alpha parallel to Jx - Jy - (Tx - Ty)parallel to(2), for all x, y epsilon E, where alpha is a nonnegative constant. An element x epsilon E is called a duality fixed point of T if Tx = Jx. The purpose of this paper is to introduce the definition of alpha-strong duality pseudocontractive mappings and to study its fixed point problem and applications for operator equation and variational inequality problems.