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

Sridarat Phikul (Faculty of Science, Chiang Mai University, Chiang Mai, Thailand)
Suantai Suthep (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand)

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 multivalued 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.

Keywords: fixed point, directed graph, multi-valued mapping, weak contraction, graph contractive mapping