Entire functions that share two pairs of small functions
In this paper, we study the unicity of entire functions and their derivatives and obtain the following result: let ff be a non-constant entire function, let a1{a}_{1}, a2{a}_{2}, b1{b}_{1}, and b2{b}_{2} be four small functions of ff such that a1≢b1{a}_{1}\not\equiv {b}_{1}, a2≢b2{a}_{2}\not\equiv {...
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2021-05-01
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Online Access: | https://doi.org/10.1515/math-2021-0011 |
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doaj-554f05690f544e6b8d37b1edfb93d4432021-10-03T07:42:35ZengDe GruyterOpen Mathematics2391-54552021-05-0119114415610.1515/math-2021-0011Entire functions that share two pairs of small functionsHuang Xiaohuang0Deng Bingmao1Fang Mingliang2Department of Mathematics, Hangzhou Dianzi University, Hangzhou310012, ChinaSchool of Financial Mathematics & Statistics, Guangdong University of Finance, Guangzhou510521, ChinaDepartment of Mathematics, Hangzhou Dianzi University, Hangzhou310012, ChinaIn this paper, we study the unicity of entire functions and their derivatives and obtain the following result: let ff be a non-constant entire function, let a1{a}_{1}, a2{a}_{2}, b1{b}_{1}, and b2{b}_{2} be four small functions of ff such that a1≢b1{a}_{1}\not\equiv {b}_{1}, a2≢b2{a}_{2}\not\equiv {b}_{2}, and none of them is identically equal to ∞\infty . If ff and f(k){f}^{\left(k)} share (a1,a2)\left({a}_{1},{a}_{2}) CM and share (b1,b2)\left({b}_{1},{b}_{2}) IM, then (a2−b2)f−(a1−b1)f(k)≡a2b1−a1b2\left({a}_{2}-{b}_{2})f-\left({a}_{1}-{b}_{1}){f}^{\left(k)}\equiv {a}_{2}{b}_{1}-{a}_{1}{b}_{2}. This extends the result due to Li and Yang [Value sharing of an entire function and its derivatives, J. Math. Soc. Japan. 51 (1999), no. 7, 781–799].https://doi.org/10.1515/math-2021-0011unicityentire functionsderivativessmall functions30d3539a32 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Huang Xiaohuang Deng Bingmao Fang Mingliang |
spellingShingle |
Huang Xiaohuang Deng Bingmao Fang Mingliang Entire functions that share two pairs of small functions Open Mathematics unicity entire functions derivatives small functions 30d35 39a32 |
author_facet |
Huang Xiaohuang Deng Bingmao Fang Mingliang |
author_sort |
Huang Xiaohuang |
title |
Entire functions that share two pairs of small functions |
title_short |
Entire functions that share two pairs of small functions |
title_full |
Entire functions that share two pairs of small functions |
title_fullStr |
Entire functions that share two pairs of small functions |
title_full_unstemmed |
Entire functions that share two pairs of small functions |
title_sort |
entire functions that share two pairs of small functions |
publisher |
De Gruyter |
series |
Open Mathematics |
issn |
2391-5455 |
publishDate |
2021-05-01 |
description |
In this paper, we study the unicity of entire functions and their derivatives and obtain the following result: let ff be a non-constant entire function, let a1{a}_{1}, a2{a}_{2}, b1{b}_{1}, and b2{b}_{2} be four small functions of ff such that a1≢b1{a}_{1}\not\equiv {b}_{1}, a2≢b2{a}_{2}\not\equiv {b}_{2}, and none of them is identically equal to ∞\infty . If ff and f(k){f}^{\left(k)} share (a1,a2)\left({a}_{1},{a}_{2}) CM and share (b1,b2)\left({b}_{1},{b}_{2}) IM, then (a2−b2)f−(a1−b1)f(k)≡a2b1−a1b2\left({a}_{2}-{b}_{2})f-\left({a}_{1}-{b}_{1}){f}^{\left(k)}\equiv {a}_{2}{b}_{1}-{a}_{1}{b}_{2}. This extends the result due to Li and Yang [Value sharing of an entire function and its derivatives, J. Math. Soc. Japan. 51 (1999), no. 7, 781–799]. |
topic |
unicity entire functions derivatives small functions 30d35 39a32 |
url |
https://doi.org/10.1515/math-2021-0011 |
work_keys_str_mv |
AT huangxiaohuang entirefunctionsthatsharetwopairsofsmallfunctions AT dengbingmao entirefunctionsthatsharetwopairsofsmallfunctions AT fangmingliang entirefunctionsthatsharetwopairsofsmallfunctions |
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1716846030971994112 |