Fixed Point of Strong Duality Pseudocontractive Mappings and Applications
Baowei Liu · Abstract and Applied Analysis · 2012
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.