RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES WITH THEIR DIFFERENCE OPERATORS
RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES WITH THEIR DIFFERENCE OPERATORS
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DOI：
10.4134/bkms.2015.52.5.1401
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发表时间：
2015-09
影响因子：
0.5
通讯作者：
Xiao-Min Li;H. Yi;Cong-Yun Kang
中科院分区：
文献类型：
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作者：
Xiao-Min Li;H. Yi;Cong-Yun Kang
在有限级的限制下，证明了非常数亚纯函数与其差分算子分担三个值的两个唯一性定理，这两个定理是（6）中定理2.1关于有限级亚纯函数与其移位算子分担三个值的相应定理. 1.引言和主要结果在本文中，亚纯函数，我们将始终意味着亚纯函数在复平面上。我们采用亚纯函数的Nevan-linna理论的标准符号，如（5），（10）和（16）中所解释的。用E表示有限线性测度的任何正真实的数的集合将是方便的，不一定每次出现时都相同。对于非常数亚纯函数h，T（r，h）表示h的Nevanlinna特征线，S（r，h）表示满足S（r，h）= o（T（r，h））的任意量，当r → ∞，r6 ∈E.设f和g是两个非常数亚纯函数，a是扩张平面上的一个值。我们说f和g共享a CM的值，前提是f和g具有相同的重数和相同的a点。我们说f和g共享值a IM，假设f和g具有相同的a点，忽略重数（参见。（16））。在本文中，我们用f（f）表示f的阶（cf. (5)，（10）和（16））。我们还需要以下两个定义：定义1.1（（15））。设f是非常数亚纯函数。我们定义f的差分算子为
Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in (6) for a finite-order meromorphic function and its shift operator. 1. Introduction and main results In this paper, by meromorphic functions we will always mean meromorphic functions in the complex plane. We adopt the standard notations of the Nevan- linna theory of meromorphic functions as explained in (5), (10) and (16). It will be convenient to let E denote any set of positive real numbers of finite lin- ear measure, not necessarily the same at each occurrence. For a nonconstant meromorphic function h, we denote by T(r,h) the Nevanlinna characteristic of h and by S(r,h) any quantity satisfying S(r,h) = o(T(r,h)), as r → ∞,r 6∈E. Let f and g be two nonconstant meromorphic functions, and let a be a value in the extended plane. We say that f and g share the value a CM, provided that f and g have the same a-points with the same multiplicities. We say that f and g share the value a IM, provided that f and g have the same a-points ignoring multiplicities (cf. (16)). Throughout this paper, we denote by �(f) the order of f (cf. (5), (10) and (16)). We also need the following two definitions: Definition 1.1 ((15)). Let f be a nonconstant meromorphic function. We define difference operators of f as