Li, Xiao-Min; Ullah, Rahman; Piao, Da-Xiong; Yi, Hong-Xun Meromorphic functions sharing a nonzero value with their derivatives. (English) Zbl 1320.30060 Kyungpook Math. J. 55, No. 1, 137-147 (2015). Summary: Let \(f\) be a transcendental meromorphic function of finite order in the plane such that \(f^{(m)}\) has finitely many zeros for some positive integer \(m\geq 2\). Suppose that \(f^{(k)}\) and \(f\) share \(a\) CM, where \(k\geq1\) is a positive integer, \(a\not=0\) is a finite complex value. Then \(f\) is an entire function such that \(f^{(k)}-a=c(f-a)\), where \(c\not=0\) is a nonzero constant. The results in this paper are concerning a conjecture of R. Brück [Result. Math. 30, No.1–2, 21–24 (1996; Zbl 0861.30032)]. An example is provided to show that the results in this paper, in a sense, are the best possible. MSC: 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory Keywords:meromorphic functions; order of growth; shared values; uniqueness theorems Citations:Zbl 0861.30032 PDFBibTeX XMLCite \textit{X.-M. Li} et al., Kyungpook Math. J. 55, No. 1, 137--147 (2015; Zbl 1320.30060) Full Text: DOI