Geodesic
On exact triangle inequalities in $(q_1,q_2)$-quasimetric spaces
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 125, pp. 33-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : $(q_1,q_2)$-quasimetric space. 
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     title = {On exact triangle inequalities in $(q_1,q_2)$-quasimetric spaces},
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Z. T. Zhukovskaya; S. E. Zhukovskiy; R. Sengupta. On exact triangle inequalities in $(q_1,q_2)$-quasimetric spaces. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 125, pp. 33-38. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_125_a2/

[1] A. V. Arutyunov, A. V. Greshnov, “Teoriya $(q_1, q_2)$-kvazimetricheskikh prostranstv i tochki sovpadeniya”, DAN, 469:5 (2016), 527–531 | Zbl

[2] A. V. Arutyunov, Lectures on Convex and Set-Valued Analysis, Fizmatlit, Moscow, 2014 (In Russian)