In a metric space with a directed graph G, Jachymski (Proc Am Math Soc 1(136):1359–1373, 2008) introduced the concept of Banach G-contraction and proved two fixed point theorems for such mappings.… Expand

Latif and Abdou [7] recently proved some fixed point theorem for multivalued mappings in a complete metric space. We strengthen their results and use our results to give an improvement on the fixed… Expand

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.… Expand

We discuss two results for Caristi-type cyclic mappings due to Du and Karapinar [3]. We show that they can be deduced from our best proximity point theorem. Our result can be regarded as a… Expand