Schwarzian Norm Estimate for Functions in Generalized Robertson Class

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