REMARKS ON FIXED POINT THEOREMS IN HYPERCONVEX SPACES

Abstract

We generalize and improve known fixed point theorems in hyperconvex spaces by applying the selection theorem in [BO] and other results on C-spaces or G-convex spaces. In fact, we obtain generalizations of fixed point theorems for nonexpansive multimaps, the Kakutani type maps, and the Fan-Browder type maps. Some additional new observations are also stated for the Caristi-Kirk-Browder type theorems.