Selections of Bounded Variation
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| 024 | 7 | 0 | |a 10.1515/JAA.2004.1 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/JAA.2004.1 | ||
| 100 | 1 | |a Chistyakov |D V. V. |u Department of Mathematics, State University Higher School of Economics, Bol'shaya Pechërskaya St. 25, Nizhny Novgorod 603600, RUSSIA. e-mail: czeslaw@mail.ru | |
| 245 | 1 | 0 | |a Selections of Bounded Variation |h [Elektronische Daten] |c [V. V. Chistyakov] |
| 520 | 3 | |a 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. | |
| 540 | |a © Heldermann Verlag | ||
| 690 | 7 | |a Generalized variation |2 nationallicence | |
| 690 | 7 | |a set-valued mappings |2 nationallicence | |
| 690 | 7 | |a selection principle |2 nationallicence | |
| 690 | 7 | |a regular selections |2 nationallicence | |
| 690 | 7 | |a multivalued superposition operators |2 nationallicence | |
| 773 | 0 | |t Journal of Applied Analysis |d Walter de Gruyter GmbH & Co. KG |g 10/1(2004-06), 1-82 |x 1425-6908 |q 10:1<1 |1 2004 |2 10 |o JAA | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/JAA.2004.1 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/JAA.2004.1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Chistyakov |D V. V. |u Department of Mathematics, State University Higher School of Economics, Bol'shaya Pechërskaya St. 25, Nizhny Novgorod 603600, RUSSIA. e-mail: czeslaw@mail.ru | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Applied Analysis |d Walter de Gruyter GmbH & Co. KG |g 10/1(2004-06), 1-82 |x 1425-6908 |q 10:1<1 |1 2004 |2 10 |o JAA | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||