TY - JOUR
T1 - New Inequalities on $L_{\gamma}$-Spaces
AU - Abdullah Mir, Bilal Dar & Sajad Amin Baba
JO - Analysis in Theory and Applications
VL - 4
SP - 390
EP - 400
PY - 2013
DA - 2013/11
SN - 29
DO - http://doi.org/10.4208/ata.2013.v29.n4.8
UR - https://global-sci.org/intro/article_detail/ata/4533.html
KW - Polynomial, Zygmund inequality, polar derivative.
AB - <p style="text-align: justify;">We consider for a fixed $\mu$, the class of polynomials $$P_{n,\mu,s}:=\Bigg\{ P(z) =z^s(a_nz^{n−s}+
\sum^{n-s}_{j=\mu}a_{n−j}z^{n−j−s}); 1≤\mu≤n−s\Bigg\}$$ of degree $n$, having all zeros in $|z|≤k,$ $k≤1$, with $s$-fold zeros at the origin. In this paper,
we have obtained inequalities in the reverse direction for the above class of polynomials.
Besides, extensions of some Turan-type inequalities for the polar derivative of
polynomials have been considered.</p>