Some Inequalities for the Polar Derivative of Some Classes of Polynomials

2018/04/26 by Nuttapong Arunrat, Arunrat, Nuttapong, Keaitsuda Maneeruk Nakprasit +1
Mathematics · #Mathematical functions and polynomials #Mathematical Inequalities and Applications #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1804.10203

Abstract

In this paper, we investigate an upper bound of the polar derivative of a polynomial of degree n p(z)=(z-z_m)^t_m (z-z_m-1)^t_m-1⋯ (z-z₀)^t₀(a₀+∑_ν=μ ^{n-(t_m+⋯+t₀)} a_νz^ν) where zeros z₀,…,z_m are in \z:|z|<1\ and the remaining n-(t_m+⋯+t₀ ) zeros are outside \z:|z|

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