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Meromorphic functions that share one or two values. (English) Zbl 0841.30027
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 $1, \infty \subset M$.

30D35Distribution of values (one complex variable); Nevanlinna theory