On Strongly Starlike Functions Related to the Bernoulli Lemniscate
On Strongly Starlike Functions Related to the Bernoulli Lemniscate
Let $\mathcal{S}^{\ast}_{L}(\lambda)$ be the class of functions $f$, analytic in the unit disc $\Delta=\{z:|z|<1\}$, with the normalization $f(0)=f'(0)-1=0$, which satisfy the condition\begin{equation*}\frac{zf'(z)}{f(z)}\prec \left(1+z\right)^{\lambda},\end{equation*}where $\prec$ is the subordination relation. The class $\mathcal{S}^{\ast}_{L}(\lambda)$ is a subfamily of the known class of strongly starlike functions of order $\lambda$. In this paper,the relations between …