TY - JOUR
T1 - Some $L^{\gamma}$ Inequalities for the Polar Derivative of a Polynomial
AU - A. Mir, M. Bidkham & B. Dar
JO - Analysis in Theory and Applications
VL - 1
SP - 1
EP - 10
PY - 2017
DA - 2017/01
SN - 33
DO - http://doi.org/10.4208/ata.2017.v33.n1.1
UR - https://global-sci.org/intro/article_detail/ata/4611.html
KW - Polar derivative, polynomials, $L^{\gamma}$-inequalities in the complex domain, Laguerre's theorem.
AB - <p style="text-align: justify;">In this paper, we consider an operator $D_α$ which maps a polynomial $P(z)$ in to $D_αP(z):= np(z)+(α−z)P′(z)$, where $α ∈ \mathcal{C}$ and obtain some $L^{\gamma}$&nbsp;inequalities for
lucanary polynomials having zeros in $|z|≤k≤1$. Our results yields several generalizations
and refinements of many known results and also provide an alternative proof of
a result due to Dewan et al. [7], which is independent of Laguerre’s theorem.</p>