HYBRID FIXED POINT THEORY WITH PPF DEPENDENCE IN BANACH ALGEBRAS WITH APPLICATIONS TO NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

Abstract

In this paper, a couple of hybrid fixed point theorems with PPF dependence are proved in a Banach algebra involving three systems of operators and they are then applied to some nonlinear hybrid functional differential equations of delay and neutral type for provingthe existence of PPF dependent solutions under certain mixed Lipschitz and compactness type conditions. Our abstract results as well as considered functional differential equations are new to the literature in the subject of nonlinear analysis.