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Inequalities for the Polar Derivative of a Polynomial

Complex Analysis and Operator Theory, 2010
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Liman, A., Mohapatra, R. N., Shah, W. M.
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Lγ Inequalities for the Polar Derivative of Polynomials

Malaysian Journal of Mathematical Sciences, 2023
In this paper, firstly, we obtain an inequality in Lγ analogue concerning the polar derivative for a polynomial p(ξ) = Xm ν=0 cνξν of degree m having no zero in |ξ| < r, r ≥ 1 proved by Govil et al. [15]. Secondly, we also prove Lγ version for the polar derivative of an ordinary inequality for a polynomial having all its zeros in |ξ| ≤ r, r ≤ 1 ...
Singh, M. S.   +3 more
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On the zeros of the polar derivative of a polynomial

The Journal of Analysis, 2021
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M. H. Gulzar, B. A. Zargar, S. A. Malik
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On the polar derivative of a constrained polynomial

The Journal of Analysis, 2022
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Mir, Abdullah, Gupkari, Sameer Ahmad
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Inequalities Concerning the Polar Derivative of a Polynomial

Bulletin of the Malaysian Mathematical Sciences Society, 2015
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Gulzar, Suhail, Rather, N. A.
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Inequalities for the polar derivative of a polynomial

Journal of Interdisciplinary Mathematics, 2007
Polynomials, Inequality, Polar Derivative. Abstract: In this paper we obtain new results concerning maximum modules of the polar derivative of a polynomial with restricted zeros. Our results generalize and refine upon the results of Aziz and Rather (3) and Jagjeet Kaur (9).
K. K. Dewan, Abdullah Mir
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Polarization, Polynomials, and War

Journal of Conflict Resolution, 1993
Michael Wallace reports a very pronounced curvilinear relationship between a new measure of the polarization of the state system and warfare during 1815-1964. He suggests considerable caution when interpreting the results and urges replication. This is a replication.
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Extremal Problems for a Polynomial and Its Polar Derivative

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2023
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NEW REGION FOR ZEROS OF A POLAR DERIVATIVE OF POLYNOMIAL

jnanabha
Let P(z) := Pn j=0 aj z j be a polynomial of degree n. Then by Cauchy’s Classical result, all zeros of P(z) lie in |z| ≤ 1 + max 0≤j≤n−1 | aj an | . In this paper, we shall extend such results to polar derivative of an algebraic polynomial.
Mohammad, R.   +2 more
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