Extensions of Bernstein Type Inequalities of a Polynomial to Polar Derivative | Chapter 4 | Theory and Practice of Mathematics and Computer Science Vol. 1

 

Let p (z) be a polynomial of degree n and a be any real or complex number, the polar derivative of p(z) ,

denoted by D p(z) a , is defined as

Da p(z) = np(z)+ (a - z)p¢(z).

In this Chapter, we discuss the simple and short proofs of the Bernstein type inequalities on polar derivative of a

polynomial obtained by Dewan and Singh [J. of Combinatorics, Information & System Sciences, 31(2006)(1-4),

317-324.] compared to related existing results and further worthy implications of the techniques involved.

Author (s) Details

Barchand Chanam

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

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