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

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Matematicheskie Zametki, 2002, Volume 71, Issue 4, Pages 611–632
DOI: https://doi.org/10.4213/mzm372 (Mi mzm372)

This article is cited in 19 scientific papers (total in 19 papers)

Multi-Valued Mappings of Bounded Generalized Variation

V. V. Chistyakov

N. I. Lobachevski State University of Nizhni Novgorod

Full-text PDF (334 kB) Citations (19)

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

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.

Received: 02.02.2000
Revised: 09.02.2001

English version:
Mathematical Notes, 2002, Volume 71, Issue 4, Pages 556–575
DOI: https://doi.org/10.1023/A:1014892001168

Bibliographic databases:

UDC: 517.518.24+515.124

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm372

https://doi.org/10.4213/mzm372

https://www.mathnet.ru/eng/mzm/v71/i4/p611

This publication is cited in the following 19 articles:

Vyacheslav V. Chistyakov, SpringerBriefs in Optimization, From Approximate Variation to Pointwise Selection Principles, 2021, 1
Chistyakov V.V., “Asymmetric Variations of Multifunctions With Application”, J. Math. Anal. Appl., 478:2 (2019), 421–444
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
Mielke A., Roubicek T., Rate-Independent Systems, Applied Mathematical Sciences, 193, Springer, 2015, 1–660
Vyacheslav V. Chistyakov, SpringerBriefs in Mathematics, Metric Modular Spaces, 2015, 45
Vyacheslav V. Chistyakov, SpringerBriefs in Mathematics, Metric Modular Spaces, 2015, 79
Vyacheslav V. Chistyakov, SpringerBriefs in Mathematics, Metric Modular Spaces, 2015, 1
Vyacheslav V. Chistyakov, SpringerBriefs in Mathematics, Metric Modular Spaces, 2015, 93
Vyacheslav V. Chistyakov, SpringerBriefs in Mathematics, Metric Modular Spaces, 2015, 19
Vyacheslav V. Chistyakov, SpringerBriefs in Mathematics, Metric Modular Spaces, 2015, 65
Vyacheslav V. Chistyakov, Springer Proceedings in Mathematics & Statistics, 32, Models, Algorithms, and Technologies for Network Analysis, 2013, 65
Chistyakov, VV, “Modular metric spaces, I: Basic concepts”, Nonlinear Analysis-Theory Methods & Applications, 72:1 (2010), 1
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
Yu. V. Tretyachenko, V. V. Chistyakov, “Selection Principle for Pointwise Bounded Sequences of Functions”, Math. Notes, 84:3 (2008), 396–406
A. A. Vasil'eva, “Multivalent Maps with Second-Order Modulus of Continuity”, Math. Notes, 82:5 (2007), 708–712
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
Chistyakov, VV, “The optimal form of selection principles for functions of a real variable”, Journal of Mathematical Analysis and Applications, 310:2 (2005), 609
V. V. Chistyakov, “Selections of Bounded Variation”, Journal of Applied Analysis, 10:1 (2004), 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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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