Landau-type Theorems for Polyanalytic and Log-$α$-analytic functions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916987259584512 |
|---|---|
| author | Li, P. Liu, M. -S. Ponnusamy, S. Zhao, H. |
| author_facet | Li, P. Liu, M. -S. Ponnusamy, S. Zhao, H. |
| contents | In the present article, we investigate the univalence property of polyanalytic functions and $\log$-$α$-analytic functions. First, by using a new idea, we prove an improved lemma and the coefficient estimates for bounded polyanalytic functions on the unit disk. Then, we present three versions of Landau-type theorems for such functions and determine the univalence domain and the radius of schlicht disk. Finally, as a consequence, the Landau-type theorems for $\log$-$α$-analytic functions are also provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Landau-type Theorems for Polyanalytic and Log-$α$-analytic functions Li, P. Liu, M. -S. Ponnusamy, S. Zhao, H. Complex Variables Primary 30C99, Secondary: 31A30 In the present article, we investigate the univalence property of polyanalytic functions and $\log$-$α$-analytic functions. First, by using a new idea, we prove an improved lemma and the coefficient estimates for bounded polyanalytic functions on the unit disk. Then, we present three versions of Landau-type theorems for such functions and determine the univalence domain and the radius of schlicht disk. Finally, as a consequence, the Landau-type theorems for $\log$-$α$-analytic functions are also provided. |
| title | Landau-type Theorems for Polyanalytic and Log-$α$-analytic functions |
| topic | Complex Variables Primary 30C99, Secondary: 31A30 |
| url | https://arxiv.org/abs/2510.02806 |