A class of functions whose sublevel sets are absolute retracts
type: Item
instance of: scholarly article
title: A class of functions whose sublevel sets are absolute retracts
zbMATH Open document ID: 1142.54006
author: Biagio Ricceri
published in: Topology and its Applications
publication date: 2008-05-15T00:00:00Z
review text: The main result is the following theorem: Let \(E\) be a real Banach space and let \(X\subset E\) be a closed and convex set. Moreover let \(\phi :X\to {\mathcal R}\) be a lower semicontinuous convex function such that \(\phi (x_0) = 0\) and \[ \alpha = \inf _{x_0\neq x \in X}\frac{\phi (x)}{| | x - x_0| | } > 0 \] for some \(x_0\in X\). If \(J:X\to {\mathcal R}\) is a Lipschitzian function with constant \(L< \alpha \) then each nonempty sublevel set of \(\phi + J\) is an absolute retract.
reviewed by: Zbigniew Grande
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 54C55
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 5275710
zbMATH Keywords: Lipschitzian multifunction
zbMATH Keywords: Absolute retracts
zbMATH Keywords: Sublevel set
MaRDI profile type: Publication
full work available at URL: j.topol.2007.01.026
OpenAlex ID: W2014027449
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DOI: 10.1016/J.TOPOL.2007.01.026
description: scientific article; zbMATH DE number 5275710