INEQUALITIES FOR B-OPERATOR

Let Pn denote the space of all complex polynomials P(z) = Pn j=0 ajzj of degree n. Let P E Pn, for any complex number alpha, D alpha P(z) = nP(z) + (alpha - z)P'(z), denote the polar derivative of the polynomial P(z) with respect to alpha and Bn denote a family of operators that maps Pn into itself. In this paper, we combine the operators B and D alpha and establish certain operator preserving inequalities concerning polynomials, from which a variety of interesting results can be obtained as special cases.