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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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On order covering maps in ordered spaces and Chaplygin-type inequalities
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by E. S. Zhukovskiy
Translated by: S. V. Kislyakov
St. Petersburg Math. J. 30 (2019), 73-94
DOI: https://doi.org/10.1090/spmj/1530
Published electronically: December 5, 2018
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Abstract:

The study of covering mappings in partially ordered spaces, started by A. V. Arutyunov, E. S. Zhukovskiy, and S. E. Zhukovskiy (see Topology and its Applications. 2015, v. 179, no. 1) is continued. A set of order covering is defined; this set is investigated for the Nemytskiĭ operator in the space of essentially bounded measurable functions. The equation $\psi (x,x)=y$ is treated, where $\psi$ is antitonic in the second variable. In terms of the set of order covering for $\psi$ in the first variable, a theorem is obtained on the existence of solutions, on their estimates, and on the existence of a lower solution. These results are applied to an implicit integral equation, and certain statements on Chaplygin-type integral inequalities are obtained.
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Bibliographic Information
  • E. S. Zhukovskiy
  • Affiliation: G. R. Derzhavin Tambov State University, ul. Internatsional′naya 33, 392000 Tambov, Russia—and—RUDN University, ul. Mikhlukho-Maklaya 6, 117198 Moscow, Russia
  • Email: zukovskys@mail.ru
  • Received by editor(s): June 22, 2016
  • Published electronically: December 5, 2018
  • Additional Notes: This work has been accomplished under the support of the Russian Science Foundation (Project no. 15-11-10021)—§§1 and 3, of the Ministry of Science and Education of Russia (Task no. 3.8515.2017/BCh)—§4, and of the RUDN University Program “5–100”—§5
  • © Copyright 2018 American Mathematical Society
  • Journal: St. Petersburg Math. J. 30 (2019), 73-94
  • MSC (2010): Primary 47J99; Secondary 46N20, 34A09
  • DOI: https://doi.org/10.1090/spmj/1530
  • MathSciNet review: 3790745