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Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions.
- Source :
- Czechoslovak Mathematical Journal; Jul2024, Vol. 74 Issue 2, p397-414, 18p
- Publication Year :
- 2024
-
Abstract
- It is known that if f is holomorphic in the open unit disc D of the complex plane and if, for some c > 0, ∣f(z)∣ ⩽ 1/(1−∣z∣<superscript>2</superscript>)<superscript>c</superscript>, z ∈ D , then ∣f′(z)∣ ⩽ 2(c+1)/(1−∣z∣<superscript>2</superscript>)<superscript>c+1</superscript>. 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 D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00114642
- Volume :
- 74
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Czechoslovak Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 178086172
- Full Text :
- https://doi.org/10.21136/CMJ.2024.0332-23