Abstract
We prove that, in an additive inequality for norms of intermediate derivatives of functions defined on a finite segment and equal to zero at a given system of points, the least possible value of a constant coefficient of the norm of a function coincides with the exact constant in the corresponding Markov-Nikol'skii inequality for algebraic polynomials that are also equal to zero at this system of points.
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References
V. I. Burenkov, “On exact constants in the inequalities for norms of intermediate derivatives on a finite segment”,Tr. Mat. Inst. Akad. Nauk SSSR,156, 22–29 (1980).
V. F. Babenko, V. A. Kofanov, and S. A. Pichugov, “On Kolmogorov inequalities for functions defined on a finite segment”,Ukr. Mat. Zh.,47, No. 1, 105–107 (1995).
A. I. Zvyagintsev, “Inequalities with exact constants for norms of intermediate derivatives”, in:Abstracts of the International Conference “Functional Spaces, Theory of Approximations, and Nonlinear Analysis” Dedicated to the 90th Birthday of Academician S. M. Nikol'skii (Moscow, April 27–May 3, 1995) [in Russian], Moscow (1995), pp. 131–132.
A. Kh. Turetskii,Interpolation Theory in Problems [in Russian], Vol. 2, Vysheishaya Shkola, Minsk (1997).
Additional information
Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal Vol. 51, No. 1, pp. 117–119, January, 1999.
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Babenko, V.F., Uédraogo, Z.B. On exact constants in inequalities for norms of derivatives on a finite segment. Ukr Math J 51, 128–130 (1999). https://doi.org/10.1007/BF02591920
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DOI: https://doi.org/10.1007/BF02591920