Uniqueness and periodicity for meromorphic functions with partial sharing values

2019 ◽  
Vol 69 (1) ◽  
pp. 99-110
Author(s):  
Weichuan Lin ◽  
Shengjiang Chen ◽  
Xiaoman Gao
Keyword(s):  
Uniqueness Theorem ◽  
Meromorphic Functions ◽  
Sharing Values ◽  
Hyper Order

Abstract We prove a periodic theorem of meromorphic functions of hyper-order ρ2(f) < 1. As an application, we obtain the corresponding uniqueness theorem on periodic meromorphic functions. In addition, we show the accuracy of the results by giving some examples.

On Sharing Values of Meromorphic Functions and Their Differences

2011 ◽  
Vol 63 (1-2) ◽  
pp. 557-565 ◽  
Author(s):  
Zong-Xuan Chen ◽  
Hong-Xun Yi
Keyword(s):  
Meromorphic Functions ◽  
Sharing Values

scholarly journals Some Remarks on Boundary Behavior of Analytic and Meromorphic Functions

1955 ◽  
Vol 9 ◽  
pp. 79-85 ◽  
Author(s):  
F. Bagemihl ◽  
W. Seidel
Keyword(s):  
Meromorphic Function ◽  
Uniqueness Theorem ◽  
Meromorphic Functions ◽  
Boundary Behavior ◽  
Regular Function ◽  
Simple Manner ◽  
Regular Functions ◽  
Almost All ◽  
Jordan Arcs

This paper is concerned with regular and meromorphic functions in |z| < 1 and their behavior near |z| = 1. Among the results obtained are the following. In section 2 we prove the existence of a non-constant meromorphic function that tends to zero at every point of |z| = 1 along almost all chords of |z| < 1 terminating in that point. Section 3 deals with the impossibility of ex tending this result to regular functions. In section 4 it is shown that a regular function can tend to infinity along every member of a set of spirals approach ing |z| = 1 and exhausting |z| < 1 in a simple manner. Finally, in section 5 we prove that this set of spirals cannot be replaced by an exhaustive set of Jordan arcs terminating in points of |z| = 1; Theorem 3 of this section can be interpreted as a uniqueness theorem for meromorphic functions.

scholarly journals A uniqueness theorem of algebraically non-degenerate meromorphic maps into PN(C)

1976 ◽  
Vol 64 ◽  
pp. 117-147 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
Projective Space ◽  
Uniqueness Theorem ◽  
Complex Projective Space ◽  
Meromorphic Functions ◽  
Uniqueness Theorems ◽  
Meromorphic Maps ◽  
Complex Projective

In the previous paper [3], the author generalized the uniqueness theorems of meromorphic functions given by G. Pólya in [5] and R. Nevanlinna in [4] to the case of meromorphic maps of Cn into the N- dimensional complex projective space PN(C).

scholarly journals A note on power of meromorphic function and its shift operator of certain hyper-order sharing one small function and a value

2021 ◽  
Vol 55 (1) ◽  
pp. 57-63
Author(s):  
A. Banerjee ◽  
A. Roy
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Shift Operator ◽  
Small Function ◽  
A Value ◽  
Hyper Order

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing a small function together with a value which improve and complement some earlier results. In particular, more or less we have improved and extended two results of Qi-Yang [Meromorphic functions that share values with their shifts or their $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling the superfluous conclusions in them.

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