### On maximum modulus of polar derivative of a polynomial

#### Abstract

Let p(z) be a polynomial of degree n and for any real or complex number α, Dα p(z) denotes the polar derivative of p(z) with respect to α, then D

_{α}p(z) = np(z) + (α −z)p’(z). In this paper, we consider the more general class of polynomials p(z) = a_{0}+ ∑ a_{ν}z^{ν}, 1 ≤ µ ≤ n, not vanishing in |z| < k, k > 0, to estimate max |D_{α}p(z)| in terms of max |p(z)| by involving some coefficients of p(z), where 0 < r ≤ ρ ≤ k. Interestingly, the results improve and extend other well known inequalities to polar derivative. Moreover, our results give several interesting results as special cases.**Published:**2021-04-05

**How to Cite this Article:**Kshetrimayum Krishnadas, Barchand Chanam, On maximum modulus of polar derivative of a polynomial, J. Math. Comput. Sci., 11 (2021), 2650-2664 Copyright © 2021 Kshetrimayum Krishnadas, Barchand Chanam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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