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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 x₀ 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.
Β. E. Rhoades (Sat,) studied this question.