• INEQUALITIES CONCERNING THE B-OPERATORS

Abstract

In this paper we consider an operator B which carries a polynomial P(z) of degree n into B[P(z)]= λ0P(z) + λ1(nz/2)P’(z)/1! + λ2 (nz/2)2P”(z)/2! Where λ0, λ1 and λ2 are such that all the zeros of U(z)= λ0 + C(n, 1)λ1z + C(n, 2) λ2 z2 lie in the half plane |z|≤|z-n/2| and investigate the dependence of |B[P(Rz)] – α B[P(rz)]| on the minimum and the maximum modulus of P(z) on for every real or complex number α with |α|≤ 1 , R > r ≥ 1 with restriction on the zeros of the polynomial P(z) and establish some new operator preserving inequalities between polynomials.