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Polar Derivative Versions of Polynomial Inequalities

DOI: 10.4236/apm.2015.512068, PP. 745-755

Keywords: Polynomials, Polar Derivative of a Polynomial, Zeros, Extremal Polynomials

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Abstract:

Let \"\"be a polynomial of degree n and for a complex number , let \"\"?denote the polar derivative of the polynomial \"\"?with respect to . In this paper, first we extend as well as generalize the result proved by Dewan and Mir [Inter. Jour. Math. and Math. Sci., 16 (2005), 2641-2645] to polar derivative. Besides, another result due to Dewan et al. [J. Math. Anal. Appl. 269 (2002), 489-499] is also extended to polar derivative.

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