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
Selections of Bounded Variation
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.
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