Generalized Turan-type Inequalities for Polar Derivative of a Polynomial

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Mathematical Sciences and Applications E-Notes
Volume:11 Issue:4
Generalized Turan-type Inequalities for Polar Derivative of a Polynomial

Generalized Turan-type Inequalities for Polar Derivative of a Polynomial

Authors : Kshetrimayum Krishnadas, Thangjam Singh, Barchand Chanam

Pages : 178-191

Doi:10.36753/mathenot.948462

View : 126 | Download : 155

Publication Date : 2023-10-25

Article Type : Research Paper

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

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