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
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
H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and unique...H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.展开更多
By using the cone theory and the monotone succession skills, it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex condition...By using the cone theory and the monotone succession skills, it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex conditions in Banach spaces. The results presented here improve and generalize some corresponding results for increasing operator.展开更多
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
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].
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.
基金Supported by NNSF(10601022,11061021)Supported by NSF of Inner Mongolia Au-tonomous Region(200607010106)Supported by SRP of Higher Schools of Inner Mongolia(NJ10006)
文摘H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.
基金the Scientific Research Foundation of Henan Provincial Education Committee(200410483004)
文摘By using the cone theory and the monotone succession skills, it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex conditions in Banach spaces. The results presented here improve and generalize some corresponding results for increasing operator.
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].
