| On an Inequality of Pual Turan Concerning Polynomials-Ⅱ |
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| 摘 要： | Let P(z) be a polynomial of degree n and for any complex number α, let D_αP(z) = nP(z)+(α- z) P′(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.
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| 关 键 词： | Polar derivative polynomials inequalities maximum modulus growth |
On an Inequality of Pual Turan Concerning Polynomials-II |
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| Institution: | Department of Mathematics, University of Kashmir, Hazratbal Srinagar-190006, India |
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| Abstract: | Let P(z) be a polynomial of degree n and for any complex number α, let DαP(z)=nP(z)+(α?z)P′(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a poly-nomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others. |
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| Keywords: | Polar derivative polynomials inequalities maximum modulus growth |
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