In this paper, we introduce a new type of multi-valued 
-contraction mapping on a metric space endowed with a directed graph and prove an existence theorem for fixed point problems in metric space endowed with a graph. Moreover, we prove fixed point theorems in partially ordered metric spaces by our main result. Some examples illustrating our main results are also present.
| Author(s) | Kangtunyakarn, Atid, Kheawborisut, Araya, Suantai, Suthep |
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