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    • Inequalities for the derivative of a polynomial

      Abdul Aziz Nisar Ahmad

      Volume 107 Issue 2 May 1997 pp 189-196

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/107/02/0189-0196

    • Keywords

       

      Maximum modules; inequalities; polynomials

    • Abstract

       

      Let P(z) be a polynomial of degreen which does not vanish in ¦z¦ <k, wherek > 0. Fork ≤ 1, it is known that$$\mathop {\max }\limits_{|z| = 1} |P'(z)| \leqslant \frac{n}{{1 + k^n }}\mathop {\max }\limits_{|z| = 1} |P(z)|$$, provided ¦P’(z)¦ and ¦Q’(z)¦ become maximum at the same point on ¦z¦ = 1, where$$Q(z) = z^n \overline {P(1/\bar z)} $$. In this paper we obtain certain refinements of this result. We also present a refinement of a generalization of the theorem of Tuŕan.

    • Author Affiliations

       

      Abdul Aziz1 Nisar Ahmad1

      1. Post Graduate Department of Mathematics, University of Kashmir, Hazratbal 190 006, Kashmir, India

    • Dates

       
      Published
      May 1997
      Manuscript received
      28 February 1996
      Manuscript revised
      5 June 1996
      Final version published online
      1 May 1997

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