A graphical version of Reich s fixed point theorem

In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0; 1];X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.