Normal families of meromorphic functions with multiple values
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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 $D$.
Abstract
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 $D$.
참고문헌 (10)
- H. H. Chen, "Normality criterion and singular directions", Conf. Proc. Lecture Notes Anal., pp.34~40 (1994), Internat. Press
- M. L. Fang, "Normality criteria for a family of meromorphic functions", Acta Math. Sinica, 37(1), pp.86~90 (1994)
- Y. X. Gu, "Normal Families and its Application" (2007), Science Press
- W. K. Hayman, "Meromorphic Functions" (1964), Clarendon Press
- J. Schiff, "Normal Families" (1993), Springer-Verlag
- G. F. Xue, "A criterion for normality of a family of meromorphic functions", J. East China Norm. Univ. Natur. Sci. Ed, 2(2), pp.15~22 (1988)
- L. Yang, "A fundamental inequality and its application", Chinese Ann. Math. Ser. B, 4(3), pp.347~354 (1983)
- L. Yang, "Value Distribution Theory", pp.1993, Springer
- L. Zalcman, "Normal families: New perspectives", Bull. Amer. Math. Soc, 35(3), pp.215~230 (1998)
- L. J. Zhao, "Normal families of meromorphic functions and multiple values", Acta Math. Sci. Ser. A. Chin. Ed, 35(2), pp.256~263 (2015)