FIXED POINT THEOREMS FOR α-ψ-CONTRACTIONS ON METRIC SPACES WITH A GRAPH

In 2008 Jachymski used the context of metric spaces endowed with a graph in theory of fixed points in some general structures and In 2012, Samet introduced a new concept of α-ψ-contractive type mappings and established fixed point theorems for such mappings in complete metric spaces. The purpose of this article is to compose this two contexts and present some new fixed point results for α-ψ-contraction on complete metric spaces endowed with a graph and in finally, as a consequence of our main result, we obtain fixed point theorems for cyclic contractive mappings.