University of MaraghehSahand Communications in Mathematical Analysis2322-580707120170701$G$-asymptotic contractions in metric spaces with a graph and fixed point results75832394610.22130/scma.2017.23946ENKamalFallahiDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.0000-0003-3400-4424Journal Article20170114In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metric spaces endowed with a graph.https://scma.maragheh.ac.ir/article_23946_19404569cb84bcaf00c0dcb506605188.pdf