Article
| Title: | Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions (English) |
| Author: | Bhowmik, Bappaditya |
| Author: | Sen, Sambhunath |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 397-414 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | It is known that if $f$ is holomorphic in the open unit disc ${\mathbb D}$ of the complex plane and if, for some $c>0$, $|f(z)|\leq 1/(1-|z|^2)^c$, $z\in {\mathbb D}$, then $|f'(z)|\leq 2(c+1)/(1-|z|^2)^{c+1}$. We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in ${\mathbb D}$. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class. (English) |
| Keyword: | Bloch function |
| Keyword: | meromorphic function |
| Keyword: | Landau's reduction |
| Keyword: | Taylor coefficient |
| MSC: | 30C50 |
| MSC: | 30C99 |
| MSC: | 30D45 |
| DOI: | 10.21136/CMJ.2024.0332-23 |
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| Date available: | 2024-07-10T14:50:57Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152448 |
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