Inequalities Concerning the Polar Derivative of a Polynomial

Article

Abstract

In this paper, certain refinements and generalizations of some inequalities concerning the polynomials and their polar derivative are obtained.

Keywords

Polynomials Inequalities in the complex domain Polar derivative Bernstein’s inequality 

Mathematics Subject Classification

30A10 30C10 30C15 

Notes

Acknowledgments

The authors are highly grateful to the referee for his commendable suggestions and comments.

References

  1. 1.
    Aziz, A.: Inequalities for the polar derivative of a polynomial. J. Approx. Theo. 55, 183–193 (1988)CrossRefMATHGoogle Scholar
  2. 2.
    Aziz, A., Dawood, Q.M.: Inequalities for a polynomial and its derivatives. J. Approx. Theory 54, 306–311 (1998)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Aziz, A., Shah, W.M.: An integral mean estimate for polynomial. Indian J. Pure Appl. Math. 28, 1413–1419 (1997)MathSciNetMATHGoogle Scholar
  4. 4.
    Chan, T.N., Malik, M.A.: On Erdös-Lax theorem. Proc. Indian Acad. Sci. 92, 191–193 (1983)MathSciNetMATHGoogle Scholar
  5. 5.
    Dewan, K.K., Singh, Naresh, Mir, Abdullah: Extensions of some polynomial inequalities to the polar derivative. J. Math. Anal. Appl. 352, 807–815 (2009)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Lax, P.D.: Proof of a conjecture of P. Erdös on the derivative of a polynomial. Bull. Am. Math. Soc. 50, 509–513 (1944)CrossRefMATHGoogle Scholar
  7. 7.
    Gardner, R.B., Govil, N.K., Weems, A.: Some results concerning rate of growth of polynomials, East. J. Approx. 10, 301–312 (2004)MathSciNetMATHGoogle Scholar
  8. 8.
    Govil, N.K.: On the growth of polynomials. J. Inequal. Appl. 7, 623–631 (2002)MathSciNetMATHGoogle Scholar
  9. 9.
    Govil, N.K.: Some inequalities for derivatives of polynomials. J. Approx. Theory 66(1), 29–35 (1991)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Govil, N.K., Rahman, Q.I., Schmeisser, G.: On the derivative of a polynomial, Illinois. J. Math. 23, 319–329 (1979)MathSciNetMATHGoogle Scholar
  11. 11.
    Malik, M.A.: On the derivative of a polynomial. J. Lond. Math. Soc. Second Ser. 1, 57–60 (1969)CrossRefMATHGoogle Scholar
  12. 12.
    Milovanovic, G.V., Mitrinovic, D.S., Rassias, ThM: Topics in Polynomials: Extremal Properties, Inequalities, Zeros. World scientific Publishing Co., Singapore (1994)CrossRefMATHGoogle Scholar
  13. 13.
    Qazi, M.A.: On the maximum modulus of polynomials. Proc. Am. Math. Soc. 115, 337–343 (1992)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Rahman, Q.I., Schmessier, G.: Analytic Theory of Polynomials. Claredon Press, Oxford (2002)Google Scholar
  15. 15.
    Rather, N.A., Gulzar, Suhail: Refinements of some inequalities concerning the polar derivative of a polynomial. Funct. Approx. Comment. Math. 51, 269–283 (2014)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Schaffer, A.C.: Inequalities of A. Markoff and S. Bernstein for polynomials and related functions. Bull. Am. Math. Soc. 47, 565–579 (1941)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Turán, P.: Uber die Ableitung von Polynomen. Compositio Mathematica 7, 89–95 (1939)MathSciNetMATHGoogle Scholar

Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Department of Comptuer Science and EngineeringIslamic University of Science and TechnologyAwantiporaIndia
  2. 2.Department of MathematicsUniversity of KashmirSrinagarIndia

Personalised recommendations