A NEW DIFFERENTIAL INEQUALITY

Abstract

A NEW DIFFERENTIAL INEQUALITY

Abstract

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

Keywords

• Differential subordination,Dominant

References

1. Miller, S. S. and Mocanu, P. T. Differential Subordinations. Theory and Applications (Marcel Dekker Inc., New York, Basel, 2000).
2. Oros, Gh. I. On a differential inequality II, General Mathematics 10 (1-2), 33–36, 2002.
3. Oros, Gh. I. and C˘ata¸s, A. A new differential inequality I, General Mathematics 11 (1-2), 47–52, 2003.