• Inequalities for the derivative of a polynomial

    • Fulltext


        Click here to view fulltext PDF

      Permanent link:

    • 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

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2023-2024 Indian Academy of Sciences, Bengaluru.