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Journal of Applied Analysis

Editor-in-Chief: Liczberski, Piotr / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

2 Issues per year


CiteScore 2017: 0.33

SCImago Journal Rank (SJR) 2017: 0.183
Source Normalized Impact per Paper (SNIP) 2017: 0.364

Mathematical Citation Quotient (MCQ) 2017: 0.27

Online
ISSN
1869-6082
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Volume 10, Issue 1

Issues

Selections of Bounded Variation

V. V. Chistyakov
  • Department of Mathematics, State University Higher School of Economics, Bol'shaya Pechërskaya St. 25, Nizhny Novgorod 603600, RUSSIA. e-mail:
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Published Online: 2010-06-09 | DOI: https://doi.org/10.1515/JAA.2004.1

Abstract

The paper presents recent results concerning the problem of the existence of those selections, which preserve the properties of a given set-valued mapping of one real variable taking on compact values from a metric space. The properties considered are the boundedness of Jordan, essential or generalized variation, Lipschitz or absolute continuity. Selection theorems are obtained by virtue of a single compactness argument, which is the exact generalization of the Helly selection principle. For set-valued mappings with the above properties we obtain a Castaing-type representation and prove the existence of multivalued selections and selections which pass through the boundaries of the images of the set-valued mapping and which are nearest in variation to a given mapping. Multivalued Lipschitzian superposition operators acting on mappings of bounded generalized variation are characterized, and solutions of bounded generalized variation to functional inclusions and embeddings, including variable set-valued operators in the right hand side, are obtained.

Key words and phrases.: Generalized variation; set-valued mappings; selection principle; regular selections; multivalued superposition operators

About the article

Received: 2002-10-14

Revised: 2003-08-01

Published Online: 2010-06-09

Published in Print: 2004-06-01


Citation Information: Journal of Applied Analysis, Volume 10, Issue 1, Pages 1–82, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/JAA.2004.1.

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