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

Pub Date : 2024-05-31 DOI:10.21136/cmj.2024.0332-23
Bappaditya Bhowmik, Sambhunath Sen
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Abstract

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)∣ ⩽ 1/(1−∣z2)c, \(z \in \mathbb{D}\), then ∣f′(z)∣ ⩽ 2(c+1)/(1−∣z2)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.

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某些分形函数的导数和分形布洛赫型函数的界限
众所周知,如果 f 在复平面的开放单位圆盘 (\mathbb{D}\)中是全态的,并且对于某些 c >;0,∣f(z)∣ ⩽ 1/(1-∣z∣2)c, \(z \in \mathbb{D}\),那么∣f′(z)∣ ⩽ 2(c+1)/(1-∣z∣2)c+1。我们考虑了这一结果的分形类似物。此外,我们还引入并研究了一类在 D 中具有非零简单极点的布洛赫类函数。
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