Common fixed point for multivalued ($\psi$-$G$)-contraction mappings in partial metric spaces with a graph structure

In the present work, we first discuss the definition of a multivalued ($\psi$-$G$)-contraction mapping in a metricspace endowed with a graph as introduced in \cite{1} and we suggest a generalization. Then, we prove a common fixed point theorem for multivalued ($\psi$-$G$)-contraction mappings in partial metric spaces endowed with a graph. An example of application illustrates the main existence result and some known existence results are derived.