New Fixed Point Results with PPF Dependence in Banach Spaces Endowed with a Graph

We introduce the concept of an αc‐admissible non‐self‐mappings with respect to ηc and establish the existence of PPF dependent fixed and coincidence point theorems for αcηc‐ψ‐contractive non‐self‐mappings in the Razumikhin class. As applications of our PPF dependent fixed point and coincidence point theorems, we derive some new fixed and coincidence point results for ψ‐contractions whenever the range space is endowed with a graph or with a partial order. The obtained results generalize, extend, and modify some PPF dependent fixed point results in the literature. Several interesting consequences of our theorems are also provided.