Linear convex sets and curves in linear norm
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 1, pp. 10-17.

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The generalization of the concept of a convex set is considered in the article to the case of spaces with the linear norm. The linear trigonometry is investigated and the form of several classical curves is found in the linear norm.
Keywords: convex set, linear norm, linear triangle.
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E. G. Belov; N. D. Livanov. Linear convex sets and curves in linear norm. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 1, pp. 10-17. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a1/

[1] A. C. Thompson, Minkowski Geometry, Cambridge Univ. Press, Cambridge, New York, Melbourne, 1996, 358 pp. | MR | Zbl

[2] A. Ziya, R. Kaya, “On the Taxicab Trigonometry”, J. of Inst. of Mathematics and Computer Sciences, 10:3 (1997), 151–159 | MR | Zbl

[3] Y. P. Ho, Y. Liu, “Parabolas in Taxicab Geometry”, Missouri J. of Mathematical Sciences, 8 (1996), 63–72 | MR | Zbl

[4] J. Moser, J. Kramer, “Lines and parabolas in Taxicab Geometry”, The Pi Mu Epsilon J., 7 (1982), 441–444

[5] E. G. Belov, “Linear-convex graphs and some root-game problems”, Bulletin of Chelyabinsk State University, 26:280 (2013), 21–32

[6] K. Thompson, T. Dray, “Taxicab angles and trigonometry”, The Pi Mu Epsilon J., 11:2 (2000), 87–96 | MR