Critical Values and Moduli of the Derivative of a Complex Polynomial at its Zeros

Critical Values and Moduli of the Derivative of a Complex Polynomial at its Zeros

Under some constraints on the critical values of an algebraic polynomial with complex coefficients, a sharp inequality for the product of certain powers of moduli of its derivative at its zeros is established. The equality is attained for a suitable Chebyshev polynomial of the first kind.

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2017-09, Vol.225 (6), p.877-882
1. Verfasser: Dubinin, V. N.
Format: Artikel
Sprache:eng
Schlagworte:
Chebyshev approximation
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
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Zusammenfassung:Under some constraints on the critical values of an algebraic polynomial with complex coefficients, a sharp inequality for the product of certain powers of moduli of its derivative at its zeros is established. The equality is attained for a suitable Chebyshev polynomial of the first kind.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-017-3503-4