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

## Abstract

T. A. Burton presented in some examples of integral equations a notion of progressive contractions on C([a, ∞[). 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 C([a, b], B) and C([a, ∞[, B) where B 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.

## Authors

Veronica Ilea
Department of Mathematics Babes-Bolyai University , Faculty Mathematics and Computer Science, Cluj-Napoca, Romania

Diana Otrocol
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy
Technical University of Cluj-Napoca, Romania

## Keywords

G-contraction; step by step contraction; Picard operator; weaakly Picard operator; generalized fibre contraction theorem; functional differential equation; functional integral equation; equation with maxima.

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##### Cite this paper as:

V. Ilea, D. Otrocol, Functional differential equations with maxima, via step by step contraction principle, Carpathian J. Math., 37 (2021) no. 2, pp. 195-202, DOI: 10.37193/CJM.2021.02.05

##### Journal

Carpathian J. Mathematics

1584 – 2851

1843 – 4401