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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

DOI: 10.13447/j.1674-5647.2019.04.07

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 = {Guo , DongAo , EnTang , Huo and Xiong , Liangpeng}, 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 $\cal C$.

Guo , DongAo , EnTang , Huo and Xiong , Liangpeng. (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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