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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n1.1}, url = {http://global-sci.org/intro/article_detail/ata/4611.html} }