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Russian Universities Reports. Mathematics, 2019, Volume 24, Issue 125, Pages 33–38
DOI: https://doi.org/10.20310/1810-0198-2019-24-125-33-38 (Mi vtamu95) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Scientific articles

On exact triangle inequalities in $(q_1,q_2)$-quasimetric spaces

Z. T. Zhukovskayaa, S. E. Zhukovskiyba, R. Senguptaa

a RUDN University
b V. A. Trapeznikov Institute of Control Sciences of RAS
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DOI: https://doi.org/10.20310/1810-0198-2019-24-125-33-38
Abstract: For arbitrary $(q_1,q_2)$-quasimetric space, it is proved that there exists a function $f,$ such that $f$-triangle inequality is more exact than any $(q_1,q_2)$-triangle inequality. It is shown that this function $f$ is the least one in the set of all concave continuous functions $g$ for which $g$-triangle inequality hold.
Keywords: $(q_1,q_2)$-quasimetric space.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00106
19-01-00080
Russian Science Foundation 17-11-01168
The work is partially supported by the Russian Foundation for Basic Research (projects no. 18-01-00106_a, 19-01-00080_a). The results of Section 3 are due to the second author who was supported by the Russian Science Foundation (project no. 17-11-01168).
Received: 24.01.2019
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: Z. T. Zhukovskaya, S. E. Zhukovskiy, R. Sengupta, “On exact triangle inequalities in $(q_1,q_2)$-quasimetric spaces”, Russian Universities Reports. Mathematics, 24:125 (2019), 33–38
Citation in format AMSBIB
\Bibitem{ZhuZhuSen19}
\by Z.~T.~Zhukovskaya, S.~E.~Zhukovskiy, R.~Sengupta
\paper On exact triangle inequalities in $(q_1,q_2)$-quasimetric spaces
\jour Russian Universities Reports. Mathematics
\yr 2019
\vol 24
\issue 125
\pages 33--38
\mathnet{http://mi.mathnet.ru/vtamu95}
\crossref{https://doi.org/10.20310/1810-0198-2019-24-125-33-38}
\elib{https://elibrary.ru/item.asp?id=37526678}
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    • This publication is cited in the following 2 articles:
    1. E. S. Zhukovskiy, “Geometric progressions in distance spaces; applications to fixed points and coincidence points”, Sb. Math., 214:2 (2023), 246–272  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. T. V. Zhukovskaya, V. Merchela, “Ob ustoichivosti i nepreryvnoi zavisimosti ot parametra mnozhestva tochek sovpadeniya dvukh otobrazhenii, deistvuyuschikh v prostranstvo s rasstoyaniem”, Vestnik rossiiskikh universitetov. Matematika, 27:139 (2022), 247–260  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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