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林珊华 《泉州师范学院学报》2011,29(2):37-42,54
从权弱分担的角度分析亚纯函数(或整函数)fn与其k阶导数[fn](k)的唯一性问题,得到f(n)=[fn](k)且f=cexp((λ/n)z)(c为非需常数,λk=1)的充分条件. 相似文献
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LI Yun-tong CAO Yao 《重庆大学学报(英文版)》2007,6(4):283-286
The uniqueness problem of entire functions sharing one small function was studied. By Picard’s Theorem, we proved that for two transcendental entire functions f (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), if f n(z)(f(z)-1)f′(z) and gn(z)(g(z)-1)g′(z) share a(z) CM, 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]. 相似文献
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证明了有穷下级非常数整函数f和g分担有穷的2个CM公共值的唯一性,替换了M.Ozawa所证定理中的条件,结论比M.Ozawa的结论更强. 相似文献
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QIAO Lei 《重庆大学学报(英文版)》2007,6(2):146-150
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. 相似文献
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段曦盛 《重庆大学学报(英文版)》2003,2(2)
Introduction Let f and g be two meromorphic functions defined in the open complex plane C, and k be a nonnegative integer or infinity. For {}aC违U, denote by (;)kEaf the set of all a-points of f where an a-point of multiplicity m is counted m times if mk and otherwise k+1 times. If (;)(;)kkEafEag=, then, f and g are considered to share the value a with weight k, which is expressed by f and g share (a ,k). Clearly if f and g share (a ,k), then they share (a ,p) for all integer p in 0pk#. It… 相似文献
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林珊华 《泉州师范学院学报》2007,25(2):30-35
权弱分担是定义在“CM”和“IM”之间的一个新概念.文章主要采用权弱分担的思想讨论两个亚纯函数具有公共小函数的唯一性问题,并获得了三个唯一性定理. 相似文献
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林珊华 《泉州师范学院学报》2010,28(2):1-5
采用权弱分担值的思想讨论两个亚纯函数fnf′,gng′权弱分担有理函数的唯一性,得到:设p(z),q(z)为两个互质的n1,n2次多项式,f,g为两个非常数超越亚纯函数,如果fnf′与gng′分担"(pq((zz)),m)"且(1)当2≤m≤∞时,满足n≥max{11,2n1+4n2+3};(2)当m=1时,满足n≥max{13,2n1+4n2+3};(3)当m=0时,满足n≥max{23,2n1+4n2+3},则f=c1Q(z)exp(α(z)),g=c2Q-1(z)exp(-α(z)),其中:c1,c2为2个常数且Q(z)是有理函数;α(z)为满足(c1c2)n+1(Q′(z)/Q(z)+α′(z))2≡(p(z)/q(z))2的多项式,或者f=tg,t为常数且满足tn+1=1. 相似文献
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翁东东 《赣南师范学院学报》2003,(6):10-11
在L.A.Rubel、C.C.Yang、Muse和Sleinmentz、AmerH.H.Al-Khalad等结论的基础上,讨论了关于整函数唯一性定理中分担值的问题,得到了一些新的结论. 相似文献
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LAI Li-ping LI Chun-hong 《重庆大学学报(英文版)》2007,6(4):278-282
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 f 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 Academi? Scientiarum Fennic? 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)]. 相似文献
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在涉及重级的情况下,研究有穷非整数级亚纯函数唯一性,所得的结论推广并改进了陈桂玲、张晓斌等人的一些结果. 相似文献
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研究了分担一个值且具有一个亏量等式的亚纯函数的惟一性问题 .讨论了对任何 2个非常数亚纯函数f(z) ,g(z)只要满足 :δ(0 ,f) +δ(0 ,g) +δ(∞ ,f) +δ(∞ ,g) =3或者δ2 (0 ,f) +δ2(0 ,g) +δ2 (∞ ,f) +δ2 (∞ ,g) =3且E(1,f) =E(1,g) ,那么 ,f(z) ,g(z)必定具有 5种情形之一 . 相似文献
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曹春芳 《河北职业技术学院学报》2010,(3)
运用Nevanlinna理论和值分布理论中的知识讨论了亚纯函数关于Gross问题的唯一性问题,通过改变亏量条件(及极点的个数)减少IM分担集中的元素个数。亏量越大,集合中的元素个数越少,反之亦成立。 相似文献
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