First-order Schwartian derivative and some classes of univalent functions

In this paper we give estimate of $\mathrm{\mid }{S}_f^{\mathrm{\prime }}(0)\mathrm{\mid }$, where $S_f(z)={\left(\frac{f^{\mathrm{\prime }\mathrm{\prime }}(z)}{f^{\mathrm{\prime }}(z)}\right)}^{\mathrm{\prime }}-\frac{1}{2}{\left(\frac{f^{\mathrm{\prime }\mathrm{\prime }}(z)}{f^{\mathrm{\prime }}(z)}\right)}^2$ is the Schwartian derivative, and $f$ belongs to different classes of functions univalent in the open unit disc $\text{ID}$.