(untitled) (Analysis in Theory and Applications, 2017)
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 ∈ C and obtain some L^γ 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.