Georgia Irina Oros:A new particular second-order nonlinear differential subordination, p.157-162

Abstract:

We find conditions on the complex-valued functions $A,B,C,D$ in the unit disc $U$ such that the differential inequality

$$\vert A(z)z^2 p''(z)+B(z)p^2(z)+C(z)p(z)+D(z)\vert<M$$

implies $\vert p(z)\vert<N$, where $p$ is analytic in $U$, with $p(0)=0$.

Key Words: Differential subordination, dominant.

2000 Mathematics Subject Classification: Primary: 30C80.

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