Abstract
We present a description of convex curves, which enables one to reduce the problem of approximation of a convex curve by piecewise circular lines in the Hausdorff metric to the problem of approximation of 2π-periodic functions by trigonometric splines in the uniform metric. We describe certain properties of convex curves.
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REFERENCES
I. I. Artobolevskii, Theory of Machines and Mechanisms [in Russian], Nauka, Moscow (1988).
K. von Leichtweiß, Konvexe Mengen [Russian translation], Nauka, Moscow (1985).
T. Kubota, “Ñber die Schwerpunkte der konvexen geschlossenen Kurven und Flächen,” Tôhoku Math. J., 14, 20–27 (1918).
N. P. Korneichuk, A. A. Ligun, and V. F. Babenko, Extremal Properties of Polynomials and Splines, Nova, New York (1996).
A. A. Ligun and A. A. Shumeiko, Asymptotic Methods for Reconstruction of Curves [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1997).
I. M. Yaglom and V. G. Boltyanskii, Convex Figures [in Russian], Gostekhizdat, Moscow (1951).
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Ligun, A.A., Shumeiko, A.A. Description of Convex Curves. Ukrainian Mathematical Journal 52, 1040–1057 (2000). https://doi.org/10.1023/A:1005273515824
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DOI: https://doi.org/10.1023/A:1005273515824