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.NJYT18A14), 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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Abstract: 
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 eightshaped region in the righthalf 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. 
Citation: 
DOI:10.3770/j.issn:20952651.2021.02.003 
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