Mean value theorems for correspondences
type: Item
instance of: scholarly article
title: Mean value theorems for correspondences
zbMATH Open document ID: 1011.49017
author: Jean-Paul Penot
published in: Acta Mathematica Vietnamica
publication date: 2003-05-21T00:00:00Z
review text: Starting from some properties satisfied by the normal cone \(N(S,x)\) to a subset \(S\) of a real Banach space \(X\) and \(x\in X\), the author defines axiomatically the notion of normal sprout \(\hat N^*(S,x)\). A typical example of a normal sprout is \(\hat N^*(S,x) = \partial d_S(x), \) where \(d_S\) denotes the distance function to the set \(S\). He defines also the notion of coderivative sprout of a multimapping \(F:X \rightrightarrows Y, X,Y \) Banach spaces, as a natural extension of that of coderivative, and proves some mean value results expressing, in essence, that the multimapping \(F\) satisfies locally a Lipschitz type condition with respect to the Pompeiu-Hausdorff metric. The paper ends with some open problems.
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 1799509
zbMATH Keywords: coderivative
zbMATH Keywords: Lipschitz property
zbMATH Keywords: mean value theorem
zbMATH Keywords: multimapping
zbMATH Keywords: normal cone
zbMATH Keywords: normal sprout
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1799509