Arian, AsmaRamezani, Maryam2021-11-052021-11-052019-08-01https://doi.org/10.31801/cfsuasmas.467481http://hdl.handle.net/20.500.12575/75926Let ( X , d ) be a metric space endowed with a graph G such that the set V ( G ) of vertices of G coincides with X . We define the notion of Pata- G -contraction type maps and obtain some fixed point theorems for such mappings. This extends and subsumes many recent results which were obtained for other contractive type mappings on a partially ordered metric space. As an application, we present theorem on the convergence of successive approximations for some linear operators on a Banach space.enFixed pointPicard operatorWeakly connected graphFixed point results for Pata contraction on a metric space with a graph and its applicationArticle682183118402618-6470