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Izvestiya: Mathematics, 2018, Volume 82, Issue 2, Pages 245–272
DOI: https://doi.org/10.1070/IM8546 (Mi im8546) 		 
This article is cited in 35 scientific papers (total in 35 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
English version PDF (408 kB) Citations (35) Russian version article
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DOI: https://doi.org/10.1070/IM8546
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).
Received: 14.03.2016
Revised: 04.04.2017
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 54E35, 54H25
Language: English
Original paper language: Russian
Citation: A. V. Arutyunov, A. V. Greshnov, “$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points”, Izv. Math., 82:2 (2018), 245–272
Citation in format AMSBIB
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\by A.~V.~Arutyunov, A.~V.~Greshnov
\paper $(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points
\jour Izv. Math.
\yr 2018
\vol 82
\issue 2
\pages 245--272
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    • This publication is cited in the following 35 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:73
    First page:39
     
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