Generalized contractive conditions and single valued mapping in complete metric space

Abstract

There are great number of generalizations of well-known Banach contraction mapping principle, M. Edelstein [01] was extended and defined contractive mapping. A contractive mapping is always continuous and which has a unique fixed point. M. Edelstein [01] proved that if T is a contractive mapping on a compact metric space (X,d) to itself then there exists a unique fixed point of T.