Common Fixed Point Theorems for Multi-Valued Weak Contractive Mappings in Metric Spaces with Graphs

Abstract

In this paper, a new type of graph contractive multi-valued mappings in a complete metric space with a directed graph is introduced and studied. A common fixed pointtheorem of those two multi-valued mappings is established under some appropriate conditions. Moreover, some example illustrating our main result is also given. The obtained result extends and generalizes several fixed point results of multi-valued mappings in the literature.