On coefficient problems for starlike functions related to vertical strip domains
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In the present paper, we find the sharp bound for the fourth coefficient of starlike functions $f$ which are normalized by $f(0)=0=f'(0)-1$ and satisfy the following two-sided inequality: $$ 1+ \frac{\gamma-\pi}{2\sin\gamma} < \RE \1\{ \frac{zf'(z)}{f(z)} \2\} < 1 + \frac{\gamma}{2\sin\gamma}, \quad z\in\mathbb{D}, $$ where $\mathbb{D}:=\{ z\in\mathbb{C}: |z|<1 \}$ is the unit disk and $\gamma$ is a real number such that $\pi/2 \leq \gamma <\pi$. Moreover, the sharp bound for the fifth coefficient of $f$ defined above with $\gamma$ in a subset of $[\pi/2,\pi)$ also will be found.
Abstract
In the present paper, we find the sharp bound for the fourth coefficient of starlike functions $f$ which are normalized by $f(0)=0=f'(0)-1$ and satisfy the following two-sided inequality: $$ 1+ \frac{\gamma-\pi}{2\sin\gamma} < \RE \1\{ \frac{zf'(z)}{f(z)} \2\} < 1 + \frac{\gamma}{2\sin\gamma}, \quad z\in\mathbb{D}, $$ where $\mathbb{D}:=\{ z\in\mathbb{C}: |z|<1 \}$ is the unit disk and $\gamma$ is a real number such that $\pi/2 \leq \gamma <\pi$. Moreover, the sharp bound for the fifth coefficient of $f$ defined above with $\gamma$ in a subset of $[\pi/2,\pi)$ also will be found.
참고문헌 (10)
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