Communications of the
Korean Mathematical Society CKMS

Suppose that $n$ is a positive integer. For any real number $\alpha$ ($\beta$ resp.) with $\alpha1$ resp.), let $K^{\langle n \rangle}(\alpha)$ ($K^{\langle n \rangle}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with $f(0)=f'(0)=\cdots=f^{(n-1)}(0)=f^{(n)}(0)-1=0$, Re$(\frac{zf^{(n+1)}(z)}{f^{(n)}(z)}+1) > \alpha$ (Re$(\frac{zf^{(n+1)}(z)}{f^{(n)}(z)}+1) <\beta$? resp.) in $\mathcal D$, and for any $\lambda$,

Keywords: Schwarz lemma, analytic function, univalent function, starlike function, generalized $\alpha$-convex domain, $\beta$-starlike function, region of variability, extreme point

MSC numbers: Primary 30C65, 30C45; Secondary 30C20