Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces. (11th October 2010)

• Record Type: Journal Article
• Authors: Saejung, Satit
• Other Names: Lau A. T. M. Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2010(2010)
• Publication Date: 2010-10-11
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2010/806837
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : We prove that every firmly nonexpansive-like mapping from a closed convex subsetC of a smooth, strictly convex and reflexive Banach pace into itself has a fixed point if and only ifC is bounded. We obtain a necessary and sufficient condition for the existence of solutions of an equilibrium problem and of a variational inequality problem defined in a Banach space.