Inequalities for derivatives of polynomials with restricted zeros

Author:
Attila Máté

Journal:
Proc. Amer. Math. Soc. **82** (1981), 221-225

MSC:
Primary 26C05; Secondary 26D05, 30C10

DOI:
https://doi.org/10.1090/S0002-9939-1981-0609655-8

MathSciNet review:
609655

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a polynomial of degree that has real roots all of which lie outside the interval . P. Erdös proved that if on this interval then on ; this is much stronger than the results the inequalities of A. Markov and S. N. Bernstein would give. We will show that if only roots of are restricted as above, then holds on with appropriate . An upper estimate for the best is given. Results for higher derivatives and spaces are also obtained.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0609655-8

Keywords:
Bernstein's inequality,
Markov's inequality,
polynomials with real zeros

Article copyright:
© Copyright 1981
American Mathematical Society