Lγ Inequalities for the Polar Derivative of Polynomials
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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 proved in that same paper. Our results generalize and improve some known inequalities.
polar derivative, Bernstein's inequality, polynomials, Polynomials and rational functions of one complex variable, Inequalities for trigonometric functions and polynomials, Inequalities in the complex plane, \(L^\gamma\) inequality
polar derivative, Bernstein's inequality, polynomials, Polynomials and rational functions of one complex variable, Inequalities for trigonometric functions and polynomials, Inequalities in the complex plane, \(L^\gamma\) inequality
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