Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON SUFFICIENT CONDITIONS FOR CARATHÉODORY FUNCTIONS WITH THE FIXED SECOND COEFFICIENT

  • Kwon, Oh Sang (Department of Mathematics, Kyungsung University)
  • Received : 2018.06.14
  • Accepted : 2019.01.24
  • Published : 2019.06.25
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Abstract

In the present paper, we derive several sufficient conditions for $Carath{\acute{e}}odory$ functions in the open unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ under the constraint that the second coefficient of the function is preassigned. And, we obtain some sufficient conditions for strongly starlike functions in ${\mathbb{D}}$.

Keywords

HNSHCY_2019_v41n2_227_f0001.png 이미지

FIGURE 1. The image of $\hat{p}(z)+z\hat{p}'(z)\;on\;\mathbb{D}$

HNSHCY_2019_v41n2_227_f0002.png 이미지

FIGURE 2. The image of $p_{\bar{f}}$ on $\mathbb{D}$

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