Abstract
We introduce new concepts of an alpha(c)-GF-contractive nonself-mapping, a weak alpha(c)-GF-contractive nonself-mapping, a generalized alpha(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.