A NEW DIFFERENTIAL INEQUALITY

Abstract

We find conditions on the complex-valued function A : U → C definedin the unit disc U such that the differential inequalityRe [A(z)p2(z) − α(zp0(z) − 1)2 + 2β(zp0(z))2 + γ] > 0implies Re p(z) > 0, where p ∈ H[1, n], α, β ∈ C and n is a positiveinteger.