AN OPERATOR PRESERVING INEQUALITIES BETWEEN A POLYNOMIAL AND ITS POLAR DERIVATIVES

Abstract

Let P(z) be a polynomial of degree n. In this paper we estimate the maximum and minimum modulli of the B-Operator of k^th polar derivative of P(z) in terms of the modulus of P (z) on the unit circle and there by obtain generalisations of some results recently proved by Bidkham And Mezerji. This interalia generalise the results earlier proved by Aziz and Shah, Shah and Liman and a famous conjecture of Erdös proved by Lax.