creative_2016_25_1_77_84_001

Integral inequalities concerning polynomials with polar derivatives


Mir, Abdullah and Bashir, Shahista


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creative_2016_25_1_77_84

Let P(z) be a polynomial of degree n and for any complex number \alpha, let D_\alpha P(z)=nP(z)+(\alpha-z)P^{\prime}(z) denote the polar derivative of P(z) with respect to a complex number \alpha. In this paper, we present an integral inequality for the polar derivative of a polynomial. Our theorem includes as special cases several interesting generalizations of some Zygmund type inequalities for polynomials.

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Bashir, Shahista, Mir, Abdullah