Fixed points and contraction factor functions

Abstract

In a complete metric space (X; d), we dene w-distance functions p : X X ! [0; 1), of which the metric d is a special case, and contraction factor functions r : X X ! [0; 1) such that if p(Tx;Ty) r(x; y)p(x; y) for all x; y 2 X, thenT : X ! X has a (unique) xed point.