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

Abstract

We introduce the concept of an ${\alpha }_c$-admissible non-self-mappings with respect to ${\eta }_c$ and establish the existence of PPF dependent fixed and coincidence point theorems for ${\alpha }_c{\eta }_c$-$\psi$-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 $\psi$-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.