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Zbl 0841.30027
Yi, Hong-Xun
Meromorphic functions that share one or two values.
(English)
[J] Complex Variables, Theory Appl. 28, No.1, 1-11 (1995). ISSN 0278-1077; ISSN 1563-5066/e

In this paper, the author continues his researches on the relationships of two nonconstant meromorphic functions $f,g$ that share one or two values $CM$. It is shown that if $f$ and $g$ share $ICM$ satisfying the condition: $$\lim_{r \in I} \sup N_2 (r, 1/f) + N_2 (1,f) + N_2 (r, 1/g) + N_2 (r, g)/T(r) < 1,$$ where $T(r) = \max \{T(r, f), T(r, g)\}$ and $I$ is a set of $r$ values of infinite linear measure, then $f \equiv g$ or $fg \equiv 1$. With slight variation of the above condition, the same conclusions hold when $f$ and $g$ share $1, \infty \subset M$.
[C.-C.Yang (Kowloon)]
MSC 2000:
*30D35 Distribution of values (one complex variable)

Keywords: Möbius transformation; lacunary; share value

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