Generalized Turan-type Inequalities for Polar Derivative of a Polynomial

Year 2023, Volume: 11 Issue: 4, 178 - 191, 25.10.2023

Kshetrimayum Krishnadas , Thangjam Singh Barchand Chanam

https://doi.org/10.36753/mathenot.948462

Abstract

Let $P(z)=a_0+\sum\limits_{\nu=\mu}^na_{\nu}z^{\nu}$, $1\leq\mu\leq n$, be a polynomial of degree $n$ having all its zeros in $|z|\leq k$, $k\geq 1$. We obtain an improvement and a generalization of an inequality in polar derivative proved by Somsuwan and Nakprasit [1]. Further, we also extend a result proved by Chanam and Dewan [2] to its polar version. Besides, our results are also found to generalize and improve some known inequalities.

Keywords

Turan type inequality, Polynomial, Polar Derivative, Maximum Modulus

References

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