Far East Journal of Mathematical Sciences (FJMS)

The Far East Journal of Mathematical Sciences (FJMS) publishes original research papers and survey articles in pure and applied mathematics, statistics, mathematical physics, and other related fields. It welcomes application-oriented work as well.

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BERNSTEIN TYPE INEQUALITIES FOR THE POLAR DERIVATIVE OF A CLASS OF POLYNOMIALS

Authors

  • N. Reingachan
  • Barchand Chanam

Keywords:

polynomial, zero, inequality, polar derivative

DOI:

https://doi.org/10.17654/0972087123006

Abstract

The goal of this paper is to extend as well as to improve an inequality of Bernstein type to polar derivative of a polynomial.

Received: January 16, 2023 
Accepted: February 6, 2023 

References

A. Aziz, Inequalities for the polar derivative of a polynomial, J. Approx. Theory 55(2) (1988), 183-193.

S. Bernstein, Sur la limitation des dérivées des polynomes, Comptes Rendus de l’Académie des Sciences 190 (1930), 338-340.

B. Chanam, An improved version of a theorem of S. Bernstein, J. of Global Research in Math. Archives 2(11) (2014), 1-7.

K. K. Dewan and A. Mir, Note on a theorem of S. Bernstein, Southeast Asian Bull. Math. 31(4) (2007), 691-695.

N. K. Govil, On the theorem of S. Bernstein, J. Math. Phys. Sci. 14 (1980), 183-187.

N. K. Govil and Q. I. Rahman, Functions of exponential type not vanishing in a half-plane and related polynomials, Trans. Amer. Math. Soc. 137 (1969), 501-517.

P. D. Lax, Proof of a conjecture of P. Erdös on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509-513.

M. A. Malik, On the derivative of a polynomial, J. London Math. Soc. 1 (1969), 57-60.

M. Marden, Geometry of Polynomials, Math. Surveys, Vol. 3, Amer. Math. Soc., Providence, 1966.

G. V. Milovanovic, D. S. Mitrinovic and T. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.

Published

2023-02-11

Issue

Section

Articles

How to Cite

BERNSTEIN TYPE INEQUALITIES FOR THE POLAR DERIVATIVE OF A CLASS OF POLYNOMIALS. (2023). Far East Journal of Mathematical Sciences (FJMS), 140(2), 89-97. https://doi.org/10.17654/0972087123006

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