A comparison of various definitions of contractive mappings

Abstract

A number of authors have defined contractive type mappings on a complete metric space X which are generalizations of the well-known Banach contraction, and which have the property that each such mapping has a unique fixed point. The fixed point can always be found by using Picard iteration, beginning with some initial choice x 0 ∈ X {x_0} \in X . In this paper we compare this multitude of definitions. X denotes a complete metric space with distance function d, and f a function mapping X into itself.