OPERATORS PRESERVING INEQUALITIES BETWEEN THE POLYNOMIALS

Abstract

In this paper, by combining the operators B and D_α, we investigate the dependence of B[D_α(P(Rz)−βP(z))] on the maximum modulus of P(z) on |z| = 1 for every real or complex numbers α and β with |α| ≥ 1, |β| ≤ 1 and R > 1. Our results include not only some known polynomial inequalities as special case, but also the results recently proved by Bidkham and Mezerji as a particular case.