In this article, we extend the classic Banach contraction principle to a complete metric space equipped with a partial order. We accomplish this by establishing some coincidence point for h-non decreasing self mapping satisfying certain rational type contractions in the framework of a metric space equipped with partial order. These contributions extend the existing literature on metric spaces and fixed point theory. Through illustrative examples, we showcase the practical applicability of our proposed notions and results. In addition, we present applications of our main results for a self mapping involving the integral type contractions.
