Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces
Satit Saejung · Fixed Point Theory and Applications · 2010
Abstract We prove that every firmly nonexpansive-like mapping from a closed convex subset "Equation missing" of a smooth, strictly convex and reflexive Banach pace into itself has a fixed point if and only if "Equation missing" 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.