Selections of bounded variation

• Autorzy: Chistyakov V. V.
• Języki publikacji: EN

Abstrakty

EN

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. Bibliography contains 113 items.

Słowa kluczowe

EN

generalized variation; set-valued mapping; selection principle; regular selections; multivalued superposition operators

PL

uogólnione zmiany; zestaw wartości odwzorowania; zasada wyboru; prawidłowy wybór; wielowartościowe operatory superpozycji

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2004
• Tom: Vol. 10, nr 1
• Strony: 1--82
• Opis fizyczny: Bibliogr. 113 poz.

Twórcy

autor

Chistyakov V. V.

• Department of Mathematics State University Higher School of Economics Bol`shaya Pecherskaya St. 25 Nizhny Novgorod 603600 Russia,

Bibliografia

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