Functional differential equations with maxima, via step by step contraction principle

T. A. Burton presented in some examples of integral equations a notion of progressive contractions on In 2019, I. A. Rus formalized this notion (I. A. Rus, Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle, Advances in the Theory of Nonlinear Analysis and its Applications, 3 (2019) No. 3, 111–120), put “step by step” instead of “progressive” in this notion, and give some variant of step by step contraction principle in the case of operators with Volterra property on and where is a Banach space. In this paper we use the abstract result given by I. A. Rus, to study some classes of functional differential equations with maxima.