Directionally pseudo-Lipschitz set-valued mappings
type: Item
instance of: scholarly article
title: Directionally pseudo-Lipschitz set-valued mappings
zbMATH Open document ID: 1012.49016
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-06-15T00:00:00Z
review text: A set-valued mapping \(M\) from a Hausdorff topological vector space \(E\) into a normed vector space \(F\) is called directionally pseudo-Lipschitz if the function \(\Delta _{M}:F\times F\rightarrow {\mathbb R}\) given by \(\Delta _{M}(x,y) =d(y,M(x))\) is directionally Lipschitz in the sense of [\textit{R. T. Rockafellar}, Proc. Lond. Math. Soc. (3) 39, 331--355 (1979; Zbl 0413.49015)]. The authors establish a geometric characterization of these mappings and study their tangential regularity by using three suitable notions of tangent cones introduced in the paper.
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 1744275
zbMATH Keywords: set-valued mappings
zbMATH Keywords: directional Lipschitzness
zbMATH Keywords: tangent cones
zbMATH Keywords: tangential regularity
author: Messaoud Bounkhel
author: L. Thibault
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7707
OpenAlex ID: W2087790194
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DOI: 10.1006/JMAA.2001.7707
description: scientific article; zbMATH DE number 1744275