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Matematicheskie Zametki, 1968, Volume 3, Issue 4, Pages 431–440
(Mi mzm6699)
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Some inequalities of the V. A. Markov type
V. A. Andreeva, V. M. Chevskii
Abstract:
Let $B$ be a domain in the complex plane, let $p_n(z)$ and $P_n(z)$ be polynomials of degree $n$ where the zeros of $P_n(z)$ lie in $\overline B$, let $\varphi(z)$ be a finite function, $\varphi(z)\ne0$, $z\overline\in\overline B$. We consider the problem of estimating from above the functions $L[p_n(z)]=\varphi p_n'(z)-wp_n(z),\,\overline\in\overline B$, если $|p_n(z)|\leqslant+|P_n(z)|$ при $z\in\overline B$. Under some very general conditions on $B$, $z$, $\varphi(z)$ and $w$ we prove the inequality $|L[p_n(z)]|\leqslant|L[P_n(z)]|$.
Received: 29.06.1967
Citation:
V. A. Andreeva, V. M. Chevskii, “Some inequalities of the V. A. Markov type”, Mat. Zametki, 3:4 (1968), 431–440; Math. Notes, 3:4 (1968), 275–280
Linking options:
https://www.mathnet.ru/eng/mzm6699 https://www.mathnet.ru/eng/mzm/v3/i4/p431
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