%0 Journal Article %T $G$-asymptotic contractions in metric spaces with a graph and fixed point results %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Fallahi, Kamal %D 2017 %\ 07/01/2017 %V 07 %N 1 %P 75-83 %! $G$-asymptotic contractions in metric spaces with a graph and fixed point results %K $G$-asymptotic contraction %K Orbitally $G$-continuous self-map %K Fixed point %R 10.22130/scma.2017.23946 %X In 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. %U https://scma.maragheh.ac.ir/article_23946_19404569cb84bcaf00c0dcb506605188.pdf