
Summary: In this paper, we study the problem of normal families and deduce some results, which improve and generalize several related theorems obtained by \textit{X. Pang} [Analysis, München 22, No. 2, 175--182 (2002; Zbl 1030.30030)], \textit{M. Fang} and \textit{Y. Xu} [Isr. J. Math. 129, 125--141 (2002; Zbl 1007.30025)] and \textit{F. Lü} et al. [Ann. Pol. Math. 95, No. 1, 67--75 (2009; Zbl 1170.30014)]. Mean-while, some examples are given to show the sharpness of our results.
linear differential polynomial, Nevanlinna theory, Cauchy theorem, holomorphic function, Normal functions of one complex variable, normal families, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, normal family
linear differential polynomial, Nevanlinna theory, Cauchy theorem, holomorphic function, Normal functions of one complex variable, normal families, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, normal family
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