A curvilinear cluster set uniqueness theorem for meromorphic functions

1976 ◽  
Vol 149 (3) ◽  
pp. 247-248
Author(s):  
Frederick Bagemihl
Keyword(s):  
Uniqueness Theorem ◽  
Meromorphic Functions ◽  
Cluster Set

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.

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 uniqueness problem for entire functions related to Brück’s conjecture

2018 ◽  
Vol 68 (4) ◽  
pp. 823-836
Author(s):  
Nguyen Van Thin ◽  
Ha Tran Phuong ◽  
Leuanglith Vilaisavanh
Keyword(s):  
Entire Function ◽  
Uniqueness Theorem ◽  
Nevanlinna Theory ◽  
Meromorphic Functions ◽  
Normal Family ◽  
Entire Functions ◽  
Uniqueness Problem ◽  
Family Theory

Abstract In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Brück. The above uniqueness theorem is an improvement of a problem studied by L. Z. Yang et al. [14]. However, our method differs the method of L. Z. Yang et al. [14]. We mainly use normal family theory and combine it with Nevanlinna theory instead of using only the Nevanlinna theory as in [14].

scholarly journals Intersections of Arc-Cluster Sets for Meromorphic Functions

1970 ◽  
Vol 40 ◽  
pp. 213-220 ◽  
Author(s):  
Charles L. Belna
Keyword(s):  
Unit Circle ◽  
Unit Disk ◽  
Complex Plane ◽  
Limit Point ◽  
Meromorphic Functions ◽  
Riemann Sphere ◽  
Open Unit ◽  
Open Unit Disk ◽  
Cluster Set ◽  
Jordan Arc

Let D and C denote the open unit disk and the unit circle in the complex plane, respectively; and let f be a function from D into the Riemann sphere Ω. An arc γ⊂D is said to be an arc at p∈C if γ∪{p} is a Jordan arc; and, for each t (0<t<1), the component of γ∩{z: t≤|z|<1} which has p as a limit point is said to be a terminal subarc of γ. If γ is an arc at p, the arc-cluster set C(f, p,γ) is the set of all points a∈Ω for which there exists a sequence {zk}a⊂γ with zk→p and f(zk)→a.

scholarly journals Some Note on Exceptional Values of Meromorphic Functions

1963 ◽  
Vol 22 ◽  
pp. 189-201 ◽  
Author(s):  
Kikuji Matsumoto
Keyword(s):  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Essential Singularity ◽  
Compact Set ◽  
A Value ◽  
Cluster Set ◽  
Totally Disconnected ◽  
Null Set

LetEbe a totally-disconnected compact set in thez-plane and letΩbe its complement with respect to the extendedz-plane. ThenΩis a domain and we can consider a single-valued meromorphic functionw = f(z)onΩwhich has a transcendental singularity at each point ofE. Suppose thatEis a null-set of the classWin the sense of Kametani [4] (the classNBin the sense of Ahlfors and Beurling [1]). Then the cluster set off(z)at each transcendental singularity is the wholew-plane, and hencef(z)has an essential singularity at each point ofE. We shall say that a valuewis exceptional forf(z)at an essential singularity ζ ∈Eif there exists a neighborhood of ζ where the functionf(z)does not take this valuew.

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