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We introduce new concepts of an α c -GF-contractive nonself-mapping, a weak α c -GF-contractive nonself-mapping, a generalized α c -GF-contractive nonself-mapping, and Suzuki type GF-contractions and establish the existence of PPF dependent fixed point theorems for such kind of contractive nonself-mappings in the Razumikhin class. As applications of our results, we derive some PPF dependent fixed point theorems for GF-contractive nonself-mappings whenever the range space is endowed with a graph or a partial order. The obtained results generalize, extend, and modify some PPF dependent fixed point results in the literature.

New P P F Dependent Fixed Point Theorems for Suzuki Type G F -Contractions