Radially Distributed Values and Normal Families
2018 ◽
Vol 2019
(23)
◽
pp. 7356-7378
Keyword(s):
Abstract Let L0 and L1 be two distinct rays emanating from the origin and let ${\mathcal{F}}$ be the family of all functions holomorphic in the unit disk ${\mathbb{D}}$ for which all zeros lie on L0 while all 1-points lie on L1. It is shown that ${\mathcal{F}}$ is normal in ${\mathbb{D}}\backslash \{0\}$. The case where L0 is the positive real axis and L1 is the negative real axis is studied in more detail.
Keyword(s):
1964 ◽
Vol 14
(2)
◽
pp. 137-141
Keyword(s):
1996 ◽
Vol 76
(10)
◽
pp. 598-600
Keyword(s):
1994 ◽
Vol 32
(2)
◽
pp. 572-590
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1989 ◽
Vol 22
(7)
◽
pp. 767-782
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1970 ◽
Vol 22
(3)
◽
pp. 486-491
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Keyword(s):
1976 ◽
Vol 54
(1)
◽
pp. 251-251
1974 ◽
Vol 11
(2)
◽
pp. 201-202
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