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

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 ∣ 2 ) c , z ∈ D , then ∣ f ′( z )∣ ⩽ 2( c +1)/(1−∣ z ∣ 2 ) c +1 . We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of mer...

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Bibliographic Details
Published in:Czechoslovak mathematical journal 2024-07, Vol.74 (2), p.397-414
Main Authors: Bhowmik, Bappaditya, Sen, Sambhunath
Format: Article
Language:English
Subjects:
Analysis
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Meromorphic functions
Ordinary Differential Equations
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Summary: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 ∣ 2 ) c , z ∈ D , then ∣ f ′( z )∣ ⩽ 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 D. In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2024.0332-23