Note on Bernstein Inequalities Concerning Complex Polynomials | Chapter 1 | Research Updates in Mathematics and Computer Science Vol. 7

 

Let p(z) be a polynomial of degree n having no zero in jzj < 1, then Erdös conjectured and later Lax [Bull. Amer. Math. Soc., 50 (1944), 509-513] prove that

This Erdös-Lax’s inequality was generalized for the first time by Malik [J. London

Math. Soc., 1(1969), 57-60] that if p(z) is a polynomial of degree n having no zero

in jzj < k, k > 1, then

For the class of polynomials not vanishing in jzj < k, k < 1, the precise estimate for

maximum of jp0(z)j on jzj = 1, in general, does not seem to be easily obtainable.

But for the particular class of polynomials having all its zeros on jzj = k, k < 1,

Govil [J. Math. and Phy. Sci., 14(1980), 183-187] was able to prove that

In this article, we compare some inequalities of later type concerning the ordinary

and polar derivatives of the polynomial.

Author (s) Details

Robinson Soraisam

Department of Mathematics, National Institute of Technology, Manipur-795004, India.

 

Prof. Barchand Chanam

Department of Mathematics, National Institute of Technology, Manipur-795004, India.

 

Please see the book here :- https://doi.org/10.9734/bpi/rumcs/v7/217