Fixed Point of Strong Duality Pseudocontractive Mappings and Applications | Zendy

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Fixed Point of Strong Duality Pseudocontractive Mappings and Applications

Author(s) -

Baowei Liu

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/623625

Subject(s) - mathematics , path (computing) , combinatorics , duality (order theory) , computer science , programming language

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,yE, where α is a nonnegative constant. An element xE 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. © 2012 Baowei Liu.

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