Some $L^{\gamma}$ Inequalities for the Polar Derivative of a Polynomial

Some $L^{\gamma}$ Inequalities for the Polar Derivative of a Polynomial

Year:    2017

Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 1–10

Abstract

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 $L^{\gamma}$ 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2017.v33.n1.1

Analysis in Theory and Applications, Vol. 33 (2017), Iss. 1 : pp. 1–10

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Polar derivative polynomials $L^{\gamma}$-inequalities in the complex domain Laguerre's theorem.