Schwarzian Norm Estimate for Functions in Robertson Class

Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}$ normalized by $f(0)=0$, $f^{\mathrm{\prime }}(0)=1$. For $-\pi \mathrm{/}2<\alpha <\pi \mathrm{/}2$, let ${\mathcal{S}}_{\alpha }$ be the subclass of $\mathcal{A}$ consisting of functions $f$ that satisfy the relation $\mathrm{R}\mathrm{e}\{e^{i\alpha }(1+z{f}^{\mathrm{\prime }\mathrm{\prime }}(z)\mathrm{/}{f}^{\mathrm{\prime }}(z))\}>0$ for $z\in \mathbb{D}$. In the present article, we determine the sharp estimate of the pre-Schwarzian and Schwarzian norms for functions in the class ${\mathcal{S}}_{\alpha }$.