New fixed point results with PPF dependence in Banach spaces endowed with a graph (Q2319159)

Summary: 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.