On certain properties of some subclasses of univalent functions

In this paper we determine the disks $\mathrm{\mid }z\mathrm{\mid }<r\le 1$ where for different classes of univalent functions, we have the property $$\mathrm{R}\mathrm{e}\{2\frac{z{f}^{\mathrm{\prime }}(z)}{f(z)}-\frac{z{f}^{\mathrm{\prime }\mathrm{\prime }}(z)}{f^{\mathrm{\prime }}(z)}\}>0(\mathrm{\mid }z\mathrm{\mid }<r)\mathrm{.}$$