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

Bappaditya Bhowmik, Sambhunath Sen (2024)

Czechoslovak Mathematical Journal

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.

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