Toeplitz Determinants for the Inverse of Starlike Functions Connected with the Sine Function
Received:February 13, 2020  Revised:August 01, 2020
Key Words: inverse of starlike function   Toeplitz determinant   sine function   upper bound
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11561001), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No.NJYT-18-A14), the Natural Science Foundation of Inner Mongolia of China (Grant No.2018MS01026), the Higher School Foundation of Inner Mongolia of China (Grant No.NJZY19211) and the Natural Science Foundation of Anhui Provincial Department of Education (Grant No.KJ2018A0833), Provincial Quality Engineering Project of Anhui Colleges and Universities (Grant No.2018mooc608), the Key Cultivated Project at School Level of the National Science Fund of Guangzhou Civil Aviation College (Grant Nos.18X0428; 18X0433).
 Author Name Affiliation Dong GUO Foundation Department, Chuzhou Vocational and Technical College, Anhui 239000, P. R. China Zongtao LI Foundation Department, Guangzhou Civil Aviation College, Guangdong 510403, P. R. China Huo TANG School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China En AO School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China
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Let $\mathcal S_{s}^{*}$ be the class of normalized functions $f$ defined in the open unit $\mathbb U=\{z\in \mathbb C:|z|<1\}$ such that the quantity $\frac{zf^{\prime}(z)}{f(z)}$ lies in an eight-shaped region in the right-half plane and satisfies the condition $\frac{zf^{\prime}(z)}{f(z)}\prec 1+\sin z~(z\in\mathbb U)$. In this paper, we aim to investigate Toeplitz determinants for the inverse of this function classes $\mathcal S_{s}^{*}$ associated with sine function.