Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

On the Picard – Lindelöf Argument and the Banach – Caccioppoli Contraction Mapping Principle

Alexander I. Bufetov, Ilya I. Zavolokin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, 119991 Moscow, Russia

Abstract: The aim of this note is to present a simple observation that a slight refinement of the contraction mapping principle allows one to recover the precise convergence rate in the Picard – Lindelöf theorem.

Keywords: Picard – Lindelöf argument, Banach – Caccioppoli contraction mapping principle, existence and uniqueness of solutions, ordinary differential equation

MSC: 46N20, 34A05, 34-03

Received: 17.06.2025
Accepted: 16.07.2025

Language: English

DOI: 10.1134/S1560354725040070

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