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Let (X, d) be a complete metric space with a directed graph G. Inspired by the work of Bojor, we introduce a new contractive type condition between a pair of mappings S, T : X → X with respect to G. In particular, if S = T , we obtain the result of Bojor. Moreover, we also establish a result under an independent hypothesis. An example showing that it is applicable in our setting but not in Bojor’s is given. AMS Subject Classification: 47H10, 54H25, 55M20

COMMON FIXED POINT THEOREMS FOR A CIRIC-REICH-RUS PAIR OF MAPPINGS IN METRIC SPACES WITH A DIRECTED GRAPH