ESSENTIAL FIXED POINTS OF THE MULTIVALUED MAPPINGS

Abstract

Let X be a compact metric space and let f be a continuous mapping of X into itself. Under an essential assumption that space X has the fixed point property, i.e., that every mapping of X into itself has at least one fixed point, M. K. Fort, Jr., has introduced the notion of an essential fixed point of f and has proved that each mapping f can be approximated arbitrarily closely by a mapping whose fixed points are all essential. We shall introduce in this note a notion of essential fixed point for multivalued mappings and shall prove a corresponding approxmation theorem without the assumption that space X has the fixed point property.