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arXiv · 2003.01557

Set shared by an entire function with its $k$-th derivatives using normal families

Molla Basir Ahamed
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Abstract

In this paper, we study a problem of non-constant entire function $ f $ that shares a set $ \mathcal{S}=\{a,b,c\} $ with its $ k $-th derivative $ f^{(k)} $, where $ a, b $ and $ c $ are any three distinct complex numbers. We have found a gap in the statement of the main result of \textit{Chang-Fang-Zalcman} \cite{Cha & Fan & al-ADM-2007} and with some help of the method used by \textit{Chang-Fang-Zalcman}, we have generalized the result of \textit{Chang-Fang-Zalcman} in a more compact form. As an application, we generalize the famous Br$\ddot{u}$ck conjecture \cite{Bru-1996} with the idea of set sharing.

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Molla Basir Ahamed. 2020-03-01. Set shared by an entire function with its $k$-th derivatives using normal families. https://arxiv.org/abs/2003.01557

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