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

Abstract EN

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.