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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.7
- 수록면
- 1,121 - 1,136 (16page)
- DOI
- 10.4134/BKMS.b230654
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초록· 키워드
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In this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for the tilted Carath\'eodory function of order $\beta$ and angle $\alpha$ ($\alpha \in (-\pi/2,\pi/2)$ and $\beta \in [0,\cos\alpha)$), which maps the unit disk $\mathbb{D}$ into the region $\{ w\in\mathbb{C}: {\rm{Re}}\{ {\rm e}^{{\rm i}\alpha} w \} > \beta \}$. Using these conditions, we also derive conditions for an analytic function that maps $\mathbb{D}$ into a sector defined by $\{ w\in\mathbb{C} : | \arg(w-\gamma) | < (\pi/2)\delta \}$, where $\gamma \in [0,1)$ and $\delta \in (0,1]$. The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in $\mathbb{D}$.
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