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.

References

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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

About this paper

Journal

Carpathian J. Mathematics

Publisher Name
Print ISSN

1584 – 2851

Online ISSN

1843 – 4401

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