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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 2, Pages 3–32 (Mi izv8546)  

This article is cited in 9 scientific papers (total in 9 papers)

$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points

A. V. Arutyunovabcd, A. V. Greshnovef

a Lomonosov Moscow State University
b Peoples Friendship University of Russia, Moscow
c Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
d Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
e Novosibirsk State University
f Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We introduce $(q_1,q_2)$-quasimetric spaces and investigate their properties. We study covering mappings from one $(q_1,q_2$)-quasimetric space to another and obtain sufficient conditions for the existence of coincidence points of two mappings between such spaces provided that one of them is covering and the other satisfies the Lipschitz condition. These results are extended to multi-valued mappings. We prove that the coincidence points are stable under small perturbations of the mappings.

Keywords: $(q_1,q_2)$-quasimetric, generalized triangle inequality, covering mappings, coincidence points, multi-valued mappings.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.962.2017/4.6
1.3087.2017/4.6
Russian Foundation for Basic Research 17-51-12064
18-01-00106
Russian Science Foundation 17-11-01168
This paper was written with the financial support of the Ministry of Science and Education of Russia (grants no. 1.962.2017/4.6 and no. 1.3087.2017/4.6), the RUPF programme ‘5-100’ and the Russian Foundation for Basic Research (grants no. 17-51-12064 and no. 18-01-00106). The results in §§ 3 and 5 were obtained by the first author with the support of the Russian Science Foundation (grant no. 17-11-01168).


DOI: https://doi.org/10.4213/im8546

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English version:
Izvestiya: Mathematics, 2018, 82:2, 245–272

Bibliographic databases:

UDC: 517.5
MSC: 54E35, 54H25
Received: 14.03.2016
Revised: 04.04.2017

Citation: A. V. Arutyunov, A. V. Greshnov, “$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points”, Izv. RAN. Ser. Mat., 82:2 (2018), 3–32; Izv. Math., 82:2 (2018), 245–272

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. Greshnov V A., “Regularization of Distance Functions and Separation Axioms on (Q(1), Q(2))-Quasimetric Spaces”, Sib. Electron. Math. Rep., 14 (2017), 765–773  mathnet  crossref  isi
    2. A. V. Greshnov, “Symmetrizations of distance functions and $f$-quasimetric spaces”, Siberian Adv. Math., 29 (2019), 202–209  mathnet  crossref  crossref
    3. E. S. Zhukovskiy, “The fixed points of contractions of $f$-quasimetric spaces”, Siberian Math. J., 59:6 (2018), 1063–1072  mathnet  crossref  crossref  isi  elib
    4. A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “Kantorovich's Fixed Point Theorem in Metric Spaces and Coincidence Points”, Proc. Steklov Inst. Math., 304 (2019), 60–73  mathnet  crossref  crossref  isi  elib
    5. A. V. Arutyunov, S. E. Zhukovskiy, K. V. Storozhuk, “The structure of the set of local minima of functions in various spaces”, Siberian Math. J., 60:3 (2019), 398–404  mathnet  crossref  crossref  isi  elib
    6. R. Sengupta, S. E. Zhukovskiy, “Minima of functions on $(q_1, q_2)$-quasimetric spaces”, Eurasian Math. J., 10:2 (2019), 84–92  mathnet  crossref
    7. A. V. Greshnov, R. I. Zhukov, “Teorema o polnote dlya $(q_1,q_2)$-kvazimetricheskikh prostranstv”, Sib. elektron. matem. izv., 16 (2019), 2090–2097  mathnet  crossref
    8. S. Benarab, E. S. Zhukovskii, V. Merchela, “Teoremy o vozmuscheniyakh nakryvayuschikh otobrazhenii v prostranstvakh s rasstoyaniem i v prostranstvakh s binarnym otnosheniem”, Tr. IMM UrO RAN, 25, no. 4, 2019, 52–63  mathnet  crossref  elib
    9. T. N. Fomenko, “Poisk nulei funktsionalov, nepodvizhnye tochki i sovpadeniya otobrazhenii v kvazimetricheskikh prostranstvakh”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2019, no. 6, 14–22  mathnet
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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