Abstract
In this paper we find the pairs of functionsg, G (g<G) such that the maximum length of the graph of polynomials of given degree contained betweeng andG is attained on one of the two snakes generated by the functionsg andG.
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References
P. Erdös, “An extremum problem concerning trigonometric polynomials,”Acta Sci. Math. (Szeged),9, 113–115 (1939).
G. K. Kristiansen, “Some inequalities for algebraic ant trigonometric polynomials,”J. London Math. Soc. (2),20, No. 2, 300–315 (1979).
B. D. Bojanov, “Proof of a conjecture of Erdös about the longest graph of a polynomial,”Proc. Amer. Math. Soc.,84, No. 1, 99–103 (1982).
A. G. Bakan,Certain Problems of Convex Analysis and Their Applications to the Theory of Functions [in Russian], Kandidat thesis in the physico-mathematical sciences, Kiev (1986).
E. P. Dolzhenko and E. A. Sevast'yanov, “On the definition of Chebyshev snakes,”Vestnik Moskov. Univ. Ser. I. Mat. Mekh. [Moscow Univ. Math. Bull.], No. 3, 49–58 (1994).
N. Sh. Zagirov, “Polynomials with extremal coefficients and snakes,”East J. Approx.,1, No. 2, 231–248 (1995).
A. A. Markov, “lectures on functions of the least deviation from zero”, in:Complete Works [in Russian], Gostekhizdat, Moscow-Leningrad (1948), pp. 244–291.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 61–69, January, 1999.
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Zagirov, N.S. Polynomials with graphs of maximum length. Math Notes 65, 51–58 (1999). https://doi.org/10.1007/BF02675009
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DOI: https://doi.org/10.1007/BF02675009