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Some Inequalities for the Polar Derivative of Some Classes of Polynomials by Arunrat, Nuttapong; Nakprasit, Keaitsuda Maneeruk is a scholarly article available to read on EtoBox.

What is Some Inequalities for the Polar Derivative of Some Classes of Polynomials about?

In this paper, we investigate an upper bound of the polar derivative of a polynomial of degree $n$ $$p(z)=(z-z_m)^{t_m} (z-z_{m-1})^{t_{m-1}}\cdots (z-z_0)^{t_0}(a_0+\sum\limits_{\nu=\mu} ^{n-(t_m+\cdots+t_0)} a_{\nu}z^\nu)$$ where zeros $z_0,\ldots,z_m$ are in $\{z:|z|<1\}$ and the remaining $n-(t_m+\cdots+t_0 )$ zeros are outside $\{z:|z|<k\}$ where $k \geq 1.$ Furthermore, we give a lower bound of this polynomial where zeros $z_0,\ldots,z_m$ are outside $\{z:|z|\leq k\}$ and the remaining $n-(t_m+\cdots+t_0 )$ zeros are in $\{z:|z|<k\}$ where $k\leq 1.$

Author

Arunrat, Nuttapong; Nakprasit, Keaitsuda Maneeruk

Published

2018

Language

EN