Support points of some classes of analytic and univalent functions

Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}$ satisfying $f(0)=0$ and $f^{\mathrm{\prime }}(0)=1$. Let $\mathcal{U}$ be the class of functions $f\in \mathcal{A}$ satisfying $$\mid f^{\mathrm{\prime }}(z){\left(\frac{z}{f(z)}\right)}^2-1\mid <1forz\in \mathbb{D},$$ and $\mathcal{G}$ denote the class of functions $f\in \mathcal{A}$ satisfying $$\mathrm{R}\mathrm{e}(1+\frac{z{f}^{\mathrm{\prime }\mathrm{\prime }}(z)}{f^{\mathrm{\prime }}(z)})>-\frac{1}{2}forz\in \mathbb{D}\mathrm{.}$$