FIXED POINT RESULTS FOR PATA CONTRACTION ON A METRIC SPACE WITH A GRAPH AND ITS APPLICATION

Abstract

Let (X; d) be a metric space endowed with a graph G such thatthe set V (G) of vertices of G coincides with X. We deÖne the notion of PataG-contraction type maps and obtain some Öxed point theorems for such mappings. This extends and subsumes many recent results which were obtained forother contractive type mappings on a partially ordered metric space. As an application, we present theorem on the convergence of successive approximationsfor some linear operators on a Banach space.