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In this paper, we consider some normality criteria concerning multiple values. Let $\mathcal{F}$ be a family of meromorphic functions defined in a domain $D$. Let $k$ be a positive integer and $\psi(z) \not \equiv 0,\infty$ be a meromorphic function in $D$. If, for each $f\in \mathcal{F}$ and $z\in D$, (1) $f(z)\neq 0$, and all of whose poles are multiple; (2) all zeros of $f^{(k)}(z)-\psi(z)$ have multiplicities at least $k+3$ in $D$; (3) all poles of $\psi(z)$ have multiplicities at most $k$ in $D$, then $\mathcal{F}$ is normal in $D$.
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참고문헌 (10)
참고문헌 신청
G. F. Xue / 1988 / A criterion for normality of a family of meromorphic functions / J. East China Norm. Univ. Natur. Sci. Ed 2 (2) : 15 ~ 22
H. H. Chen / 1994 / Normality criterion and singular directions / Conf. Proc. Lecture Notes Anal. : 34 ~ 40
J. Schiff / 1993 / Normal Families / Springer-Verlag
L. J. Zhao / 2015 / Normal families of meromorphic functions and multiple values / Acta Math. Sci. Ser. A. Chin. Ed 35 (2) : 256 ~ 263
L. Yang / 1983 / A fundamental inequality and its application / Chinese Ann. Math. Ser. B 4 (3) : 347 ~ 354
H. H. Chen / 1994 / Normality criterion and singular directions / Conf. Proc. Lecture Notes Anal. : 34 ~ 40
J. Schiff / 1993 / Normal Families / Springer-Verlag
L. J. Zhao / 2015 / Normal families of meromorphic functions and multiple values / Acta Math. Sci. Ser. A. Chin. Ed 35 (2) : 256 ~ 263
L. Yang / 1983 / A fundamental inequality and its application / Chinese Ann. Math. Ser. B 4 (3) : 347 ~ 354
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