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

Molla Basir Ahamed

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

Complex Variables 2020-03-04 v1

Authors: Molla Basir Ahamed

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.

Keywords

univalent functions function theory

Cite

@article{arxiv.2003.01557,
  title  = {Set shared by an entire function with its $k$-th derivatives using normal families},
  author = {Molla Basir Ahamed},
  journal= {arXiv preprint arXiv:2003.01557},
  year   = {2020}
}

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