The uniqueness of meromorphic functions in k-punctured complex plane

The uniqueness of meromorphic functions in k-punctured complex plane

The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identi...

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Main Authors: Xu Hong Yan, Liu San Yang
Format: Article
Language:English
Published: De Gruyter 2017-06-01
Series:Open Mathematics
Subjects:
shared-set
k-puncture
admissible meromorphic function
30d30
30d35
Online Access:https://doi.org/10.1515/math-2017-0063
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spelling doaj-34be7e786a91496b90f0a528c66ee10b2021-09-06T19:20:09ZengDe GruyterOpen Mathematics2391-54552017-06-0115172473310.1515/math-2017-0063math-2017-0063The uniqueness of meromorphic functions in k-punctured complex planeXu Hong Yan0Liu San Yang1School of mathematics and statistics, Xidian Universtiy, Xi’an, Shaanxi, 710126, ChinaSchool of mathematics and statistics, Xidian Universtiy, Xi’an, Shaanxi, 710126, ChinaThe main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).https://doi.org/10.1515/math-2017-0063shared-setk-punctureadmissible meromorphic function30d3030d35
collection DOAJ
language English
format Article
sources DOAJ
author Xu Hong Yan
Liu San Yang
spellingShingle Xu Hong Yan
Liu San Yang
The uniqueness of meromorphic functions in k-punctured complex plane
Open Mathematics
shared-set
k-puncture
admissible meromorphic function
30d30
30d35
author_facet Xu Hong Yan
Liu San Yang
author_sort Xu Hong Yan
title The uniqueness of meromorphic functions in k-punctured complex plane
title_short The uniqueness of meromorphic functions in k-punctured complex plane
title_full The uniqueness of meromorphic functions in k-punctured complex plane
title_fullStr The uniqueness of meromorphic functions in k-punctured complex plane
title_full_unstemmed The uniqueness of meromorphic functions in k-punctured complex plane
title_sort uniqueness of meromorphic functions in k-punctured complex plane
publisher De Gruyter
series Open Mathematics
issn 2391-5455
publishDate 2017-06-01
description The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).
topic shared-set
k-puncture
admissible meromorphic function
30d30
30d35
url https://doi.org/10.1515/math-2017-0063
work_keys_str_mv AT xuhongyan theuniquenessofmeromorphicfunctionsinkpuncturedcomplexplane
AT liusanyang theuniquenessofmeromorphicfunctionsinkpuncturedcomplexplane
AT xuhongyan uniquenessofmeromorphicfunctionsinkpuncturedcomplexplane
AT liusanyang uniquenessofmeromorphicfunctionsinkpuncturedcomplexplane
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