PPF dependent fixed point in modified Razumikhin class with applications

In this paper we introduce the concepts of c − C α β − admissible mapping, ( α β ) c − Θ − contraction, weak ( α β ) c − Θ − contraction, generalized ( α β ) c − Θ − contraction and establish the existence of PPF dependent fixed point theorems for such classes of contractive nonself-mappings in the Razumikhin class. We give, also, a result of existence of a PPF dependent fixed point by a condition of Suzuki type. As applications of our theorems, we deduce some PPF dependent fixed point theorems for nonself-mappings valued in a Banach space endowed with a graph or a partial order, and furnish an illustrative example to support our main theorem.