Extensions of Bernstein Type Inequalities of a Polynomial to Polar Derivative
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
Department of Mathematics, National Institute of Technology, Manipur, India.