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LI San-hua, LIU Zhong-dong, WU Gao-xiang. Normal families related to shared values[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 54-60, 75.
Citation:
LI San-hua, LIU Zhong-dong, WU Gao-xiang. Normal families related to shared values[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 54-60, 75.
LI San-hua, LIU Zhong-dong, WU Gao-xiang. Normal families related to shared values[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 54-60, 75.
Citation:
LI San-hua, LIU Zhong-dong, WU Gao-xiang. Normal families related to shared values[J]. Journal of East China Normal University (Natural Sciences), 2013, (1): 54-60, 75.
Let $\F$ be a family of meromorphic functions on a domain
$D$, $a$ and $b$ be two nonzero finite complex numbers($\frac{a}{b}$
not positive integer). If for every $f \in \F$, $f(z) = a
\Rightarrow f^{(k)}(z) = a$, and the zeros multiplicity of $f - a$
is at least $k$, and $|f(z) - a| \geq \varepsilon$ ($\varepsilon
0)$ whenever $f^{(k)}(z) = b$, then $\F$ is normal on $D$.
{1}SCHWICK W. Sharing values and normality[J]. Arch Math, 1992, 59:50-54.{2}PANG X C, ZALCMAN L. Normality and shared values[J]. Ark Mat, 2000,38: 171-182.{3}LIN W C, YI H X. Value distribution of meromorphic functionconcerning shared values[J]. Indian J Pure Appl Math, 2003, 34:535-541.{4}FANG M L, ZALCMAN L. A note on normality and shared values[J]. JAust Math Soc, 2004, 76: 141-150.{5}PANG X C, ZALCMAN L. Normal families and shared values[J]. BullLondon Math Soc, 2000, 32: 325-331.{6}HAYMAN W K. Meromorphic Functions[M]. Oxford: Clarendon Press, 1964.