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Volume 35, Issue 4
Third Hankel Determinant for the Inverse of Starlike and Convex Functions

Dong Guo, En Ao, Huo Tang & Liangpeng Xiong

Commun. Math. Res., 35 (2019), pp. 354-358.

Published online: 2019-12

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  • Abstract

Denote $\cal S$ to be the class of functions which are analytic, normalized and univalent in the open unit disk $\mathbb U=\{z\colon |z|<1\}$. The important subclasses of $\cal S$ are the class of starlike and convex functions, which we denote by $\cal S^*$ and $\cal C$. In this paper, we obtain the third Hankel determinant for the inverse of functions $f(z)=z+\sum\limits_{n=2}^{\infty}a_nz^n$ belonging to $\cal S^*$ and $\cal C$.

  • Keywords

analytic function, third Hankel determinant, inverse of starlike function, inverse of convex function.

  • AMS Subject Headings

30C45

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gd791217@163.com (Dong Guo)

  • BibTex
  • RIS
  • TXT
@Article{CMR-35-354, author = {Dong and Guo and gd791217@163.com and 5905 and Foundation Department, Chuzhou Vocational and Technical College, Chuzhou, Anhui, 239000 and Dong Guo and En and Ao and and 6248 and School of Mathematics and Statistics, Chifeng University, Chifeng, Inner Mongolia, 024000 and En Ao and Huo and Tang and and 6249 and School of Mathematics and Statistics, Chifeng University, Chifeng, Inner Mongolia, 024000 and Huo Tang and Liangpeng and Xiong and and 5908 and School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 and Liangpeng Xiong}, title = {Third Hankel Determinant for the Inverse of Starlike and Convex Functions}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {4}, pages = {354--358}, abstract = {

Denote $\cal S$ to be the class of functions which are analytic, normalized and univalent in the open unit disk $\mathbb U=\{z\colon |z|<1\}$. The important subclasses of $\cal S$ are the class of starlike and convex functions, which we denote by $\cal S^*$ and $\cal C$. In this paper, we obtain the third Hankel determinant for the inverse of functions $f(z)=z+\sum\limits_{n=2}^{\infty}a_nz^n$ belonging to $\cal S^*$ and $\cal C$.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.04.07}, url = {http://global-sci.org/intro/article_detail/cmr/13563.html} }
TY - JOUR T1 - Third Hankel Determinant for the Inverse of Starlike and Convex Functions AU - Guo , Dong AU - Ao , En AU - Tang , Huo AU - Xiong , Liangpeng JO - Communications in Mathematical Research VL - 4 SP - 354 EP - 358 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.04.07 UR - https://global-sci.org/intro/article_detail/cmr/13563.html KW - analytic function, third Hankel determinant, inverse of starlike function, inverse of convex function. AB -

Denote $\cal S$ to be the class of functions which are analytic, normalized and univalent in the open unit disk $\mathbb U=\{z\colon |z|<1\}$. The important subclasses of $\cal S$ are the class of starlike and convex functions, which we denote by $\cal S^*$ and $\cal C$. In this paper, we obtain the third Hankel determinant for the inverse of functions $f(z)=z+\sum\limits_{n=2}^{\infty}a_nz^n$ belonging to $\cal S^*$ and $\cal C$.

Dong Guo, En Ao, Huo Tang & Liangpeng Xiong. (2019). Third Hankel Determinant for the Inverse of Starlike and Convex Functions. Communications in Mathematical Research . 35 (4). 354-358. doi:10.13447/j.1674-5647.2019.04.07
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