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Bounds for the derivative of certain meromorphic functions and on meromorphic Bloch-type functions.

Authors :
Bhowmik, Bappaditya
Sen, Sambhunath
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