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.