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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/107/03/0263-0270

    • Keywords

       

      Bernstein's inequality; polar derivative of a polynomial; inequalities in the complex domain; groth of maximum modulus

    • Abstract

       

      LetP(z) be a polynomial of degreen which does not vanish in |z|<1. In this paper, we estimate the maximum and minimum moduli of thekth polar derivative ofP(z) on |z|=1 and thereby obtain compact generalizations of some known results, which among other results, yields interesting refinements of Erdos-Lax theorem and a theorem of Ankeny and Rivlin.

    • Author Affiliations

       

      Abdul Aziz1 Wali Mohammad Shah1

      1. Post-Graduate Department of Mathematics and Statistics, University of Kashmir, Hazratbal, Srinagar - 190 006, India

    • Dates

       
      Published
      August 1997
      Manuscript received
      3 April 1996
      Manuscript revised
      6 May 1997

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