The Value Distribution of Meromorphic Functions in an Angular Domain, II

1981 ◽  
Vol s2-23 (2) ◽  
pp. 287-294 ◽  
Author(s):  
Hideo Mutō
Keyword(s):  
Meromorphic Functions ◽  
Value Distribution ◽  
Angular Domain

scholarly journals On Properties of Differences Polynomials about Meromorphic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Jianming Qi ◽  
Jie Ding ◽  
Wenjun Yuan
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Special Class ◽  
Meromorphic Functions ◽  
Value Distribution ◽  
Class Difference ◽  
Difference Polynomial

We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).

scholarly journals Value distribution of meromorphic functions concerning rational functions and differences

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mingliang Fang ◽  
Degui Yang ◽  
Dan Liu
Keyword(s):  
Positive Integer ◽  
Meromorphic Function ◽  
Rational Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Rational Functions ◽  
Value Distribution ◽  
Exponent Of Convergence ◽  
Nonzero Constant ◽  
Zero Points

AbstractLet c be a nonzero constant and n a positive integer, let f be a transcendental meromorphic function of finite order, and let R be a nonconstant rational function. Under some conditions, we study the relationships between the exponent of convergence of zero points of $f-R$ f − R , its shift $f(z+nc)$ f ( z + n c ) and the differences $\Delta _{c}^{n} f$ Δ c n f .

scholarly journals Borel Directions and Uniqueness of Meromorphic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Keyu Zhang ◽  
HongYan Xu ◽  
Hongxun Yi
Keyword(s):  
Meromorphic Functions ◽  
Angular Domain ◽  
Recent Theorem ◽  
The Relationship

We investigate the relationship between Borel directions and uniqueness of meromorphic functions and obtain some results of meromorphic functions sharing four distinct values IM and one set in an angular domain containing a Borel line. Our result is an improvement of a recent theorem given by Long and Wu (2012).

Borel Directions and the Uniqueness of Algebroid Functions Dealing with Multiple Values

2021 ◽  
Vol 58 (1) ◽  
pp. 104-118
Author(s):  
Yang Tan ◽  
Qingcai Zhang
Keyword(s):  
Conformal Mapping ◽  
Meromorphic Functions ◽  
Angular Domain ◽  
Uniqueness Results ◽  
Algebroid Functions

In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.

scholarly journals Value distribution and the Lemma of the logarithmic derivative on polydiscs

1983 ◽  
Vol 6 (4) ◽  
pp. 617-669 ◽  
Author(s):  
Wilhelm Stoll
Keyword(s):  
Distribution Function ◽  
Meromorphic Functions ◽  
Logarithmic Derivative ◽  
Value Distribution ◽  
Exceptional Sets ◽  
Vector Variable

Value distribution is developed on polydiscs with the special emphasis that the value distribution function depend on a vector variable. A Lemma of the logarithmic derivative for meromorphic functions on polydiscs is derived. Here the Bergman boundary of the polydiscs is approached along cones of any dimension and exceptional sets for such an approach are defined.

scholarly journals An Inequality of Meromorphic Functions and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhaojun Wu ◽  
Yuxian Chen ◽  
Zuxing Xuan
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Angular Domain ◽  
Covering Surface

By applying Ahlfors theory of covering surface, we establish a fundamental inequality of meromorphic function dealing with multiple values in an angular domain. As an application, we prove the existence of some new singular directions for a meromorphic functionf, namely a Bloch direction and a pseudo-T direction forf.

Entire solutions of certain type of non-linear differential equations

2020 ◽  
Vol 70 (1) ◽  
pp. 87-94
Author(s):  
Bo Xue
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Nonlinear Differential Equations ◽  
Differential Polynomial ◽  
Value Distribution ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
Value Distribution Theory ◽  
Linear Differential

AbstractUtilizing Nevanlinna’s value distribution theory of meromorphic functions, we study transcendental entire solutions of the following type nonlinear differential equations in the complex plane$$\begin{array}{} \displaystyle f^{n}(z)+P(z,f,f',\ldots,f^{(t)})=P_{1}\text{e}^{\alpha_{1}z}+P_{2}\text{e}^{\alpha_{2}z}+P_{3}\text{e}^{\alpha_{3}z}, \end{array}$$where Pj and αi are nonzero constants for j = 1, 2, 3, such that |α1| > |α2| > |α3| and P(z, f, f′, …, f(t) is an algebraic differential polynomial in f(z) of degree no greater than n – 1.

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