Caristi-Banach type contraction via simulation function

In this paper we introduce the notion of a Caristi-Banach type ${\mathcal{Z}}_R^b$- contraction in the framework of $b$- metric space endowed with a transitive relation that combine the ideas of Caristi type contraction and Banach contraction with a help of simulation function. We present an example to clarify the statement of the given result.