Fixed Point of Strong Duality Pseudocontractive Mappings and Applications

Abstract EN

Let E be a smooth Banach space with the dual E∗, an operator T:E→E∗ is said to be α-strong duality pseudocontractive if x-y, Tx-Ty≤x-y, Jx-Jy-α∥Jx-Jy-Tx-Ty∥2, for all x,y∈E, where α is a nonnegative constant.

An element x∈E is called a duality fixed point of T if Tx=Jx.

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.