scholarly journals Uniqueness of meromorphic functions sharing two finite sets

2017 ◽  
Vol 15 (1) ◽  
pp. 1244-1250 ◽  
Author(s):  
Jun-Fan Chen
Keyword(s):  
Meromorphic Functions ◽  
Uniqueness Theorems ◽  
Finite Sets ◽  
Shared Sets

Abstract We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.

scholarly journals Uniqueness of meromorphic functions sharing two sets with least possible cardinalities

2019 ◽  
Vol 57 (2) ◽  
pp. 112-130
Author(s):  
Arindam Sarkar
Keyword(s):  
Meromorphic Functions ◽  
Uniqueness Theorems ◽  
Finite Sets ◽  
Shared Set ◽  
Weaker Conditions

Abstract Let f and g be two nonconstant meromorphic functions sharing two finite sets, namely S ⊂ ℂ and {∞}. We prove two uniqueness theorems under weaker conditions on ramification indices, reducing the cardinality of the shared set S and weakening the nature of sharing of the set {∞} which improve results of Fang-Lahiri [7], Lahiri [17], Banerjee -Majumder-Mukherjee [5] and others.

scholarly journals Uniqueness theorems related to weighted sharing of two sets

2018 ◽  
Vol 10 (2) ◽  
pp. 329-339
Author(s):  
Pulak Sahoo ◽  
Himadri Karmakar
Keyword(s):  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Uniqueness Theorems ◽  
Finite Sets ◽  
Weighted Sharing

Abstract Using the notion of weighted sharing of sets, we study the uniqueness problem of meromorphic functions sharing two finite sets. Our results are inspired from an article due to J. F. Chen (Open Math., 15 (2017), 1244–1250).

scholarly journals NORMALITY AND SHARED SETS

2009 ◽  
Vol 86 (3) ◽  
pp. 339-354 ◽  
Author(s):  
MINGLIANG FANG ◽  
LAWRENCE ZALCMAN
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Complex Numbers ◽  
Finite Complex ◽  
Shared Sets ◽  
Zeros Of Functions

AbstractLet ℱ be a family of meromorphic functions defined in D, all of whose zeros have multiplicity at least k+1. Let a and b be distinct finite complex numbers, and let k be a positive integer. If, for each pair of functions f and g in ℱ, f(k) and g(k) share the set S={a,b}, then ℱ is normal in D. The condition that the zeros of functions in ℱ have multiplicity at least k+1 cannot be weakened.

Uniqueness of meromorphic functions sharing two sets with finite weight ii

2010 ◽  
Vol 41 (4) ◽  
pp. 379-392
Author(s):  
Abhijit Banerjee
Keyword(s):  
Present Author ◽  
Meromorphic Functions ◽  
Uniqueness Theorems ◽  
Weighted Sharing

With the help of the notion of weighted sharing of sets we deal with the well known question of Gross and prove some uniqueness theorems on meromorphic functions sharing two sets. Our results will improve and supplement some recent results of the present author.

On Uniqueness of Dirichlet Series

2020 ◽  
Author(s):  
Bao Qin Li
Keyword(s):  
Analytic Continuation ◽  
Dirichlet Series ◽  
Finite Order ◽  
Half Plane ◽  
Complex Plane ◽  
Meromorphic Functions ◽  
Uniqueness Problem ◽  
Uniqueness Theorems

Abstract We give a characterization of the ratio of two Dirichelt series convergent in a right half-plane under an analytic condition, which is applicable to a uniqueness problem for Dirichlet series admitting analytic continuation in the complex plane as meromorphic functions of finite order; uniqueness theorems are given in terms of a-points of the functions.

scholarly journals On the Uniqueness of Meromorphic Functions on Annuli in terms of Deficiencies

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Dawei Meng ◽  
Nan Lu ◽  
Sanyang Liu
Keyword(s):  
Meromorphic Functions ◽  
Uniqueness Theorems

The purpose of this article is to study the uniqueness of meromorphic functions on annuli. Under a certain condition about deficiencies, we prove some new uniqueness theorems of meromorphic functions on the annulus A=z:1/R0<z<R0, where 1<R0≤+∞.

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