TY - JOUR
T1 - Inequalities for the Polar Derivatives of a Polynomial
JO - Analysis in Theory and Applications
VL - 4
SP - 425
EP - 432
PY - 2014
DA - 2014/11
SN - 30
DO - http://doi.org/10.4208/ata.2014.v30.n4.10
UR - https://global-sci.org/intro/article_detail/ata/4507.html
KW - Polar derivative of a polynomial, maximum modulus, Bernstein's inequality.
AB - <p style="text-align: justify;">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.</p>