Schwarzian norm estimates for some classes of analytic functions

Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ normalized by $f(0)=0$, $f'(0)=1$. In the present article, we obtain the sharp estimates of the Schwarzian norm for functions in the classes $\mathcal{G}(\beta)=\{f\in \mathcal{A}:{\rm Re\,}[1+zf''(z)/f'(z)]0$ and $\mathcal{F}(\alpha)=\{f\in \mathcal{A}:{\rm Re\,}[1+zf''(z)/f'(z)]>\alpha\}$, where $-1/2\le \alpha\le 0$. We also establish two-point distortion theorem for functions in the classes $\mathcal{G}(\beta)$ and $\mathcal{F}(\alpha)$

Coefficient Inequalities for a Subclass of p

The aim of this paper is to study the problem of coefficient bounds for a newly defined subclass of p-valent analytic functions. Many known results appear as special consequences of our work