Inequalities for the Polar Derivatives of a Polynomial

Inequalities for the Polar Derivatives of a Polynomial

Year:    2014

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 425–432

Abstract

Let $P(z)$ be a polynomial of degree $n,$ having all its zeros in $|z|\leq 1.$ In this paper, we estimate $kth$ polar derivative of $P(z)$ on $|z|=1$ and thereby obtain compact generalizations of some known results which among other things yields a refinement of a result due to Paul Turán.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2014.v30.n4.10

Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 425–432

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Polar derivative of a polynomial maximum modulus Bernstein's inequality.

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    Bibliography

    2022

    https://doi.org/10.1016/B978-0-12-811988-4.00014-1 [Citations: 0]