The Journal of Analysis

, Volume 27, Issue 4, pp 1103–1107 | Cite as

A note on Ankeny–Rivlin theorem

  • Abdullah MirEmail author
  • Imtiaz Hussain
  • Ajaz Wani
Original Research Paper


In this paper, we consider the class of polynomials not vanishing in the unit disk and obtain a result that improves the results of Dubinin, Aziz and Dawood and the classical result of Ankeny and Rivlin.


Polynomial Maximum modulus principle Zeros 

Mathematics Subject Classification

30A10 30C10 30C15 



The authors are highly grateful to the anonymous referee for the valuable suggestions regarding the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Ankeny, N.C., and T.J. Rivlin. 1955. On a theorem of S. Bernstein. Pacific Journal of Mathematics 5: 849–852.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aziz, A., and Q.M. Dawood. 1988. Inequalities for a polynomial and its derivative. Journal of Approximation Theory 54: 306–313.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Dubinin, V.N. 2007. Applications of the Schwarz lemma to inequalities for entire functions with constarints on zeros. Journal of Mathematical Sciences 143: 3069–3076.CrossRefGoogle Scholar
  4. 4.
    Milovanovic, G.V., D.S. Mitrinovic, and Th. M Rassias. 1944. Topics in polynomials. Extremal problems, Inequalities, Zeros. Singapore: World Scientific.Google Scholar

Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KashmirSrinagarIndia

Personalised recommendations