On the notion of derivo-periodicity
type: Item
instance of: scholarly article
title: On the notion of derivo-periodicity
zbMATH Open document ID: 1086.49019
author: Jan Andres
author: Dušan Bednařík
author: Karel Pastor
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-07T00:00:00Z
review text: A function \(f:\mathbb{R}\rightarrow \mathbb{R}\) is said to be almost everywhere derivo-periodic if \(f'(t)=f'(t+\omega )\) for some \(\omega > 0\) and for almost all \(t\in \mathbb{R}\). The authors of this paper obtain characterizations of almost everywhere derivo-periodic functions in the case of the functions of negligible variation on a set \(S\subset \mathbb{R} \) of (Lebesgue) measure zero, respectively for the class of generalized absolutely continuous (\(ACG_*\)) functions in the restrited sense. Next the authors prove that a De Blasi-like differentiable multivalued function is derivo-periodic if and only if it is a sum of a function of a continuous (single-valued) periodic function, linear function and a bounded interval. Derivo-periodicity in terms of the Clarke subdifferentials is also discussed. The obtained results are finally applied to differential equations and inclusions.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 26E25
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 2153751
zbMATH Keywords: derivo-periodicity
zbMATH Keywords: almost-periodicity
zbMATH Keywords: De Blasi-like differentiability
zbMATH Keywords: Clarke subdifferential
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.08.020
OpenAlex ID: W2001903003
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DOI: 10.1016/J.JMAA.2004.08.020
description: scientific article; zbMATH DE number 2153751