Geometric mean value theorems for the Dini derivative
type: Item
instance of: scholarly article
title: Geometric mean value theorems for the Dini derivative
zbMATH Open document ID: 0829.46028
DOI: 10.1016/S0022-247X(85)71120-1
author: D. Zagrodny
author: L. Gajek
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-01-21T00:00:00Z
review text: The authors introduce a new class of mean value problems, which involve geometry of the function domain. Roughly speaking, if \(f\) maps a Banach space \((X, |\cdot |)\) into \(\mathbb{R}\cup \{+\infty\}\) and \(a,b\in X\) are such that \(f(a)> f(b)\), then there is a point \(x\in B (a,|a- b|)\) at which the Dini derivative \({\mathbf d} f(x^*; h)\) is nonnegative for every direction \(h\) from some cone. The advantage of such results over standard mean value theorems is shown by examples.
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 765149
zbMATH Keywords: Dini derivative
MaRDI profile type: Publication
full work available at URL: s0022-247x(85)71120-1
OpenAlex ID: W3140615356
description: scientific article; zbMATH DE number 765149