G-ASYMPTOTIC CONTRACTIONS IN METRIC SPACES WITH A GRAPH AND FIXED POINT RESULTS

In this paper, we discuss the existence and uniqueness of xed points for G-asymptotic contractions in metric spaces en- dowed with a graph. The result given here is a new version of Kirk s xed point theorem for asymptotic contractions in metric spaces en- dowed with a graph. The given result here is a generalization of xed point theorem for asymptotic contraction from metric s paces to metric spaces endowed with a graph.

Keywords:

G-asymptotic contraction , Orbitally G-continuous self- map , Fixed point