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Mat. Zametki, 2002, Volume 71, Issue 4, Pages 611–632 (Mi mz372)  

This article is cited in 10 scientific papers (total in 10 papers)

Multi-Valued Mappings of Bounded Generalized Variation

V. V. Chistyakov

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: We study the mappings taking real intervals into metric spaces and possessing a bounded generalized variation in the sense of Jordan–Riesz–Orlicz. We establish some embeddings of function spaces, the structure of the mappings, the jumps of the variation, and the Helly selection principle. We show that a compact-valued multi-valued mapping of bounded generalized variation with respect to the Hausdorff metric has a regular selection of bounded generalized variation. We prove the existence of selections preserving the properties of multi-valued mappings that are defined on the direct product of an interval and a topological space, have a bounded generalized variation in the first variable, and are upper semicontinuous in the second variable.

DOI: https://doi.org/10.4213/mzm372

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English version:
Mathematical Notes, 2002, 71:4, 556–575

Bibliographic databases:

UDC: 517.518.24+515.124
Received: 02.02.2000
Revised: 09.02.2001

Citation: V. V. Chistyakov, “Multi-Valued Mappings of Bounded Generalized Variation”, Mat. Zametki, 71:4 (2002), 611–632; Math. Notes, 71:4 (2002), 556–575

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Balcerzak, M, “On Helly's principle for metric semigroup valued by mappings of two real variables”, Bulletin of the Australian Mathematical Society, 66:2 (2002), 245  crossref  mathscinet  zmath  isi
    2. Chistyakov, VV, “The optimal form of selection principles for functions of a real variable”, Journal of Mathematical Analysis and Applications, 310:2 (2005), 609  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. V. V. Chistyakov, “A Pointwise Selection Principle for Functions of a Single Variable with Values in a Uniform Space”, Siberian Adv. Math., 16:3 (2006), 15–41  mathnet  mathscinet  elib
    4. A. A. Vasil'eva, “Multivalent Maps with Second-Order Modulus of Continuity”, Math. Notes, 82:5 (2007), 708–712  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Yu. V. Tretyachenko, V. V. Chistyakov, “Selection Principle for Pointwise Bounded Sequences of Functions”, Math. Notes, 84:3 (2008), 396–406  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Chistyakov, VV, “Modular metric spaces, I: Basic concepts”, Nonlinear Analysis-Theory Methods & Applications, 72:1 (2010), 1  crossref  mathscinet  isi  scopus  scopus
    7. Yu. V. Tret'yachenko, “A generalization of the Helly theorem for functions with values in a uniform space”, Russian Math. (Iz. VUZ), 54:5 (2010), 35–46  mathnet  crossref  mathscinet  elib
    8. Mielke A., Roubicek T., Rate-Independent Systems, Applied Mathematical Sciences, 193, Springer, 2015, 1–660  crossref  mathscinet  zmath  isi
    9. Chistyakov V.V. Chistyakova S.A., “The Joint Modulus of Variation of Metric Space Valued Functions and Pointwise Selection Principles”, Studia Math., 238:1 (2017), 37–57  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Chistyakov V.V., “Asymmetric Variations of Multifunctions With Application”, J. Math. Anal. Appl., 478:2 (2019), 421–444  crossref  isi
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