Abstract

In this paper, we introduce the concept of $(\alpha, \psi, \xi )-G$-contractive mappings in a metric space endowed with a directed graph $G$. We investigate the existence and uniqueness of points of coincidence and common fixed points for such mappings under some conditions. Our results extend and generalize several well-known comparable results in the literature. Some examples are provided to justify the validity of our results.

Keywords: Digraph; weakly compatible mappings; point of coincidence; common fixed point.

MSC: 54H25, 47H10

Pages:  230$-$243     

Volume  71 ,  Issue  3 ,  2019