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- Title
Fixed Point of Strong Duality Pseudocontractive Mappings and Applications.
- Authors
Baowei Liu
- Abstract
Let E be a smooth Banach space with the dual E*, an operator T : E ? E* is said to be a-strong duality pseudocontractive if (x - y,Tx - Ty) = (x - y,Jx - Jy) - a\\Jx - Jy - (Tx - Ty)\\², for all x,y ∈ E, where a 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 a-strong duality pseudocontractive mappings and to study its fixed point problem and applications for operator equation and variational inequality problems.
- Subjects
FIXED point theory; DUALITY theory (Mathematics); MATHEMATICAL mappings; BANACH spaces; SMOOTHING (Numerical analysis); NUMERICAL solutions to operator equations; VARIATIONAL inequalities (Mathematics)
- Publication
Abstract & Applied Analysis, 2012, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2012/623625