Pre-Schwarzian norm estimation for functions in the Ma-Minda-type starlike and convex classes

In this paper, we establish the sharp estimates of the pre-Schwarzian norm of functions $f$ in the Ma-Minda type starlike and convex classes ${\mathcal{S}}^{\ast }(\phi )$ and $\mathcal{C}(\phi )$, respectively, whenever $\phi (z)=3\mathrm{/}(3+(\alpha -3)z-\alpha z^2)$ with $-3<\alpha \le 1$, $\phi (z)=(1+z)(1-sz)$ with $-1\mathrm{/}3\le s\le 1\mathrm{/}3$ and $\phi (z)=1+z\mathrm{/}((1-z)(1+\alpha z))$ with $0\le \alpha \le 1\mathrm{/}2$.