Strongly balanced selections
type: Item
instance of: scholarly article
title: Strongly balanced selections
zbMATH Open document ID: 0801.26002
author: H. H. Pu
author: Hwang-Wen Pu
published in: Real Analysis Exchange
publication date: 1994-11-24T00:00:00Z
review text: The notion of path derivate and derivative was introduced by \textit{A. M. Bruckner}, \textit{R. J. O'Malley}, and \textit{B. S. Thompson} [Trans. Am. Math. Soc. 283, 97-125 (1984; Zbl 0541.26003)] and the notion of selective derivate and derivative by \textit{R. J. O'Malley} [Acta Math. Acad. Sci. Hung. 29, 77-97 (1977; Zbl 0345.26003)]. In this paper a new class of selections is defined, i.e., strongly balanced selections. It is proved that every selective derivative with respect to such selections can be realized as a path derivative. The main result is the following: If \(s\) is a strongly balanced selection and \(f\) is a monotone \(s\)- differentiable function then \(f\) is differentiable in the ordinary sense. (This is not so in general).
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26A48
zbMATH DE Number: 465107
zbMATH Keywords: path derivate
zbMATH Keywords: selective derivate
zbMATH Keywords: internal intersection condition
zbMATH Keywords: monotone function
zbMATH Keywords: bilateral system of paths
zbMATH Keywords: nonporous system of paths
zbMATH Keywords: Denjoy-Clarkson property
zbMATH Keywords: selective derivative
zbMATH Keywords: path derivative
zbMATH Keywords: strongly balanced selection
reviewed by: Tomasz Natkaniec
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 465107