The contraction principle for mappings on a modular metric space with a graph.

We give a generalization of the Banach contraction principle on a modular metric space endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as the modular metric version of Jachymski's fixed point result for mappings on a metric space with a graph. [ABSTRACT FROM AUTHOR]