Meromorphic Functions Sharing a Nonzero Value with their Derivatives

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 1,  2015, pp.137-147
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.1.137
Title & Authors
Meromorphic Functions Sharing a Nonzero Value with their Derivatives
Li, Xiao-Min; Ullah, Rahman; Piao, Da-Xiong; Yi, Hong-Xun;

Abstract
Let f be a transcendental meromorphic function of finite order in the plane such that $\small{f^{(m)}}$ has finitely many zeros for some positive integer $\small{m{\geq}2}$. Suppose that $\small{f^{(k)}}$ and f share a CM, where $\small{k{\geq}1}$ is a positive integer, $\small{a{\neq}0}$ is a finite complex value. Then f is an entire function such that $\small{f^{(k)}-a=c(f-a)}$, where $\small{c{\neq}0}$ is a nonzero constant. The results in this paper are concerning a conjecture of Bruck [5]. An example is provided to show that the results in this paper, in a sense, are the best possible.
Keywords
Meromorphic functions;Order of growth;Shared values;Uniqueness theorems;
Language
English
Cited by
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