Common fixed point theorems for multi-valued weak contractive mappings in metric spaces with graphs

Abstract

© 2018, University of Nis. All rights reserved. In this paper, a new type of graph contractive multi-valued mappings in a metric space with a directed graph is introduced and studied. A common fixed point theorem of those two multi-valued mappings is established under some appropriate conditions. Moreover, some examples illustrating our main result are also given. The obtained result extends and generalizes several fixed point results of multi-valued mappings in the literature. We apply our main result to obtain common fixed point results for two multi-valued mappings in ε-chainable complete metric spaces and two cyclic contraction multi-valued mappings.