PPF dependent fixed points of generalized contractive type mappings using C-class functions with an application


Gutti Venkata Ravindranadh Babu, Madugula Vinod Kumar




In this paper, we prove the existence of PPF dependent fixed points of single-valued generalized $\alpha-\eta-\psi-\phi-F-$contraction type mappings and extend it to multi-valued $ \alpha^{*}-\psi-\phi-F-$contraction type mappings in Banach spaces. Also, we introduce the concept of $f-\alpha^{*}-$admissible mapping and prove the existence of PPF dependent coincidence points of a pair of single-valued and multi-valued mappings. A fixed point result in a Banach space endowed with a graph is obtained as an application of PPF dependent fixed point result of a single-valued mapping.