Abstract
If P(z) is a polynomial of degree n which does not vanish in |z| < 1, then it is recently proved by Rather [Jour. Ineq. Pure and Appl. Math., 9 (2008), Issue 4, Art. 103] that for every γ> 0 and every real or complex number α with |α| ≥ 1,
where D α P(z) denotes the polar derivative of P(z) with respect to α. In this paper we prove a result which not only provides a refinement of the above inequality but also gives a result of Aziz and Dawood [J. Approx. Theory, 54 (1988), 306–313] as a special case.
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Mir, A., Baba, S.A. Some integral inequalities for the polar derivative of a polynomial. Anal. Theory Appl. 27, 340–350 (2011). https://doi.org/10.1007/s10496-011-0340-z
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DOI: https://doi.org/10.1007/s10496-011-0340-z