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 {...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/554f05690f544e6b8d37b1edfb93d443 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:554f05690f544e6b8d37b1edfb93d443 |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:554f05690f544e6b8d37b1edfb93d4432021-12-05T14:10:52ZEntire functions that share two pairs of small functions2391-545510.1515/math-2021-0011https://doaj.org/article/554f05690f544e6b8d37b1edfb93d4432021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0011https://doaj.org/toc/2391-5455In 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].Huang XiaohuangDeng BingmaoFang MingliangDe Gruyterarticleunicityentire functionsderivativessmall functions30d3539a32MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 144-156 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
unicity entire functions derivatives small functions 30d35 39a32 Mathematics QA1-939 |
| spellingShingle |
unicity entire functions derivatives small functions 30d35 39a32 Mathematics QA1-939 Huang Xiaohuang Deng Bingmao Fang Mingliang Entire functions that share two pairs of small functions |
| 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]. |
| format |
article |
| author |
Huang Xiaohuang Deng Bingmao Fang Mingliang |
| 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 |
| publishDate |
2021 |
| url |
https://doaj.org/article/554f05690f544e6b8d37b1edfb93d443 |
| work_keys_str_mv |
AT huangxiaohuang entirefunctionsthatsharetwopairsofsmallfunctions AT dengbingmao entirefunctionsthatsharetwopairsofsmallfunctions AT fangmingliang entirefunctionsthatsharetwopairsofsmallfunctions |
| _version_ |
1718371644397846528 |