Multivalued superposition operators
type: Item
instance of: scholarly article
title: Multivalued superposition operators
zbMATH Open document ID: 0748.47049
author: Jürgen Appell
author: E. De Pascale
author: Peter P. Zabreĭko
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1992-09-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108237
review text: Given a bounded domain \(\Omega\) in \(\mathbb{R}^ N\), the authors study the multivalued superposition operator \(N_ F\) generated by a multivalued function \(F: \Omega\times\mathbb{R}\to 2^ \mathbb{R}\). They give continuity and boundedness conditions for \(N_ F\) in the space \(S\) of measurable functions, between two ideal function spaces, and in the space \(C\) of continuous functions. Moreover, they compare the closure \(\overline F\) and the convexification \(F^ \square\) of the function \(F\) with the closure \(\overline N_ F\) and the convexification \(N^ \square_ F\) of the corresponding operator \(N_ F\).
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 60491
zbMATH Keywords: multivalued superposition operators
zbMATH Keywords: space of measurable functions
zbMATH Keywords: multivalued superposition operator
zbMATH Keywords: continuity and boundedness conditions
zbMATH Keywords: ideal function spaces
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 60491