Sharp initial coefficient bounds and the Fekete–Szegö problem for some certain subclasses of analytic and bi-univalent functions
UDC 517.5 We introduce two new subclasses $\mathcal{U}_{\Sigma}(\alpha,\lambda)$ and ${\mathcal{B}_1}_{\Sigma}(\alpha)$ of analytic bi-univalent functions defined in the open unit disk $\mathbb{U}$, which are associated with the Bazilevich functions.  In addition, for funct...
Saved in:
| Date: | 2023 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6602 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We introduce two new subclasses $\mathcal{U}_{\Sigma}(\alpha,\lambda)$ and ${\mathcal{B}_1}_{\Sigma}(\alpha)$ of analytic bi-univalent functions defined in the open unit disk $\mathbb{U}$, which are associated with the Bazilevich functions.  In addition, for functions that belong to these subclasses, we obtain sharp bounds for the initial Taylor–Maclaurin coefficients $a_2$ and $a_3,$ as well as the sharp estimate for the Fekete–Szegö functional $a_3-\mu a_2^2.$ |
|---|---|
| DOI: | 10.37863/umzh.v75i2.6602 |