For the open question 'If two nonconstant meromorphic functions share three values IM and share a fourth value CM, then do the functions necessarily share all four values CM?', the author studies the case when...For the open question 'If two nonconstant meromorphic functions share three values IM and share a fourth value CM, then do the functions necessarily share all four values CM?', the author studies the case when four values are shared IM and their counting functions satisfy an additional condition. The author obtains some results which answer this question partially.展开更多
This paper deals with the problem of uniqueness of meromorphic functions with two deficient values and obtains a result which is an improvement of that of F.Gross and Yi Hongxun.
In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.
This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.
The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n...The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831].展开更多
The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions [ and g which are not polynominals of degree ...The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions [ and g which are not polynominals of degree less than a positive integer k, if f^nf（k）and g^ng^（k） share （1,2）, where n is another positive integer not less than k＋10, then f^nf^（k） identically equals g^ng ^（k） or f^nf^（k）g^ng^（k） identically equals 1. Particularly for k =1, we improved the results of Yang [Yang CC, Hua XH, Uniqueness and value-sharing of meromorphic functions, Annales Academiae Scientiarum Fennicae Mathematica, 1997, 22： 395-406], and Fang [Fang ML, Hua XH, Entire function that share one value, Journal of Nanjing University, 1996, 13（1）： 44-48. （In Chinese）].展开更多
A uniqueness theorem for entire functions sharing one finite complex value with weight two is proved by using Nevanlinna theory , and this improves the result of Fang and Hua.
In this paper we deal with the problem of uniqueness of meromorphic functions with two deficient values and obtain a result which is an improvement of that of F. Gross and Yi Hougxun.
The uniqueness problem of entire functions sharing one small function was studied. By Picard＇s Theorem, we proved that for two transcendental entire functionsf（z） and g（z）, a positive integer n≥9, and a（z） （n...The uniqueness problem of entire functions sharing one small function was studied. By Picard＇s Theorem, we proved that for two transcendental entire functionsf（z） and g（z）, a positive integer n≥9, and a（z） （not identically eaqual to zero） being a common small function related to f（z） and g（z）, iffn（z）（f（z）-1）f＇（z） and gn（z）（g（z）-1）g＇（z） share a（z） ca, where CM is counting multiplicity, then g（z） ≡f（z）. This is an extended version of Fang and Hong＇s theorem [ Fang ML, Hong W, A unicity theorem for entire functions concerning differential polynomials, Journal of Indian Pure Applied Mathematics, 2001, 32 （9）： 1343-1348].展开更多
In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Y...In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Yang and other authors.展开更多
Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials sh...Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1- point by proving two theorems and their related lemmas. The results extend and improve given by Fang and Hong’s theorem.展开更多
文摘For the open question 'If two nonconstant meromorphic functions share three values IM and share a fourth value CM, then do the functions necessarily share all four values CM?', the author studies the case when four values are shared IM and their counting functions satisfy an additional condition. The author obtains some results which answer this question partially.
文摘This paper deals with the problem of uniqueness of meromorphic functions with two deficient values and obtains a result which is an improvement of that of F.Gross and Yi Hongxun.
文摘In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.
基金Supported by the NSF of China(10371065)Supported by the NSF of Zhejiang Province (M103006)
文摘This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.
文摘The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831].
文摘The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions [ and g which are not polynominals of degree less than a positive integer k, if f^nf（k）and g^ng^（k） share （1,2）, where n is another positive integer not less than k＋10, then f^nf^（k） identically equals g^ng ^（k） or f^nf^（k）g^ng^（k） identically equals 1. Particularly for k =1, we improved the results of Yang [Yang CC, Hua XH, Uniqueness and value-sharing of meromorphic functions, Annales Academiae Scientiarum Fennicae Mathematica, 1997, 22： 395-406], and Fang [Fang ML, Hua XH, Entire function that share one value, Journal of Nanjing University, 1996, 13（1）： 44-48. （In Chinese）].
文摘A uniqueness theorem for entire functions sharing one finite complex value with weight two is proved by using Nevanlinna theory , and this improves the result of Fang and Hua.
文摘In this paper we deal with the problem of uniqueness of meromorphic functions with two deficient values and obtain a result which is an improvement of that of F. Gross and Yi Hougxun.
基金Funded by The National Natural Science Foundation of China under Grant No. 10671067.
文摘The uniqueness problem of entire functions sharing one small function was studied. By Picard＇s Theorem, we proved that for two transcendental entire functionsf（z） and g（z）, a positive integer n≥9, and a（z） （not identically eaqual to zero） being a common small function related to f（z） and g（z）, iffn（z）（f（z）-1）f＇（z） and gn（z）（g（z）-1）g＇（z） share a（z） ca, where CM is counting multiplicity, then g（z） ≡f（z）. This is an extended version of Fang and Hong＇s theorem [ Fang ML, Hong W, A unicity theorem for entire functions concerning differential polynomials, Journal of Indian Pure Applied Mathematics, 2001, 32 （9）： 1343-1348].
基金Foundation item: Supported by the NSF of China(10471028)Supported by the NSF of Guangdong Province(020586) Supported by the Guangzhou Education Bureau(2006, 2025)Supported by the Grant-in-Aid for Scientific Research 2004(15540151)Supported by the Japan Society for the Promotion of Science
文摘In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Yang and other authors.
文摘Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1- point by proving two theorems and their related lemmas. The results extend and improve given by Fang and Hong’s theorem.
