共查询到20条相似文献，搜索用时 203 毫秒
1.
MA Chao-weia WANG Yong-jun 《重庆大学学报(英文版)》2007,6(4):299-301
A normal theorem concerning meromorphic functions sharing values was proved with the method of Zalcman- Pang.The theorem is as follows. If for each f in F, all zeros of f-a have multiplicity at least k (k≥2), f and its k-th derivative function share a, and if f=b whenever its k-th derivative equal b, then F is normal in D. This theorem improved the result of Chen and Fang [Chen HH, Fang ML, Shared values and normal families of meromorphic functions, Journal of Mathematical Analysis and Applications, 2001, 260: 124-132]. 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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LAN Fu-xiang LI Jiang-tao 《重庆大学学报(英文版)》2007,6(4):291-293
We studied the normality conditions in families of meromorphic functions, improved the results of Fang and Zalcman [Fang ML, Zalcman L, Normal families and shared values of meromorphic functions, Computational Methods and Function Theory, 2001, 1 (1): 289-299], and generalized two new normality criterions. Let F be a family of meromorphic functions in a domain D, a a non-zero finite complex number, B a positive real number, and k and m two positive integers satisfying m>2k 4. If every function denoted by f belonging to F has only zeros with multiplicity at least k and satisfies f m(z)f (k)(z)=a??f (k)(z)?≤B or f m(z)f (k)(z)=a??f (z)?≥B, then F is normal in D. 相似文献
4.
SUN Yao-qiang MA Chao-wei 《重庆大学学报(英文版)》2007,6(4):287-290
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]. 相似文献
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证明了非常数的亚纯函数的一类非线性微分多项式具有一个非零公共值的亚纯函数的唯一性,其文结果改进了杨重骏和华歆厚的结果,扩充了方明亮的结果。 相似文献
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夏玉玲 《商丘师范学院学报》2011,27(6):22-23
研究了关于分担一个值的亚纯函数的正规族问题,证明了：设F为区域D上的亚纯函数族,k是正整数,如果对任意的f∈F.f-a的零点重数至少为k,f（z）=a■f（k）（z）=a■f（k＋1）（z）=a,则F在D上正规. 相似文献
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We studied the normality criterion for families of meromorphic functions related to shared sets. Let F be a family of meromorphic functions on the unit disc △, a and b be distinct non-zero values, S={a,b}, and k be a positive integer. If for every f∈ F, i） the zeros of f（z） have a multiplicity of at least k＋ 1, and ii） E^-f（k）（S） lohtain in E^-f（S）, then F is normal on .4. At the same time, the corresponding results of normal function are also proved. 相似文献
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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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李忠广 《绵阳师范学院学报》2011,30(5)
通过研究亚纯函数的Nevanlinna值分布理论问题,并结合亚纯函数的小函数,及其微分单项式和微分多项式,得到一比较有趣的关于亚纯函数的计数函数密指量和微分多项式的不等式,此不等式改进了Fang,Yang及I Lahiri和S.Dewan等学者的结果。 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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利用NevanLinna的亚纯函数的值分布理论,研究了超越亚纯函数微分多项式的值分布理论,取得以下主要结果:若f(z)是复平面上超越严亚纯函数,m、n和k都是正整数,且n≥2,Qj[f](j=1,2…,m)为f(z)的微分单项式,Q[f]=sum from j=1 to m ()aj(z)Qj[f]为f(z)的拟微分多项式,aj(z)是f(z)的小函数,令F(z)=Q[f](f(k)(z))n-c,则T(T,f(k)≤k+1/n(k=1)/(R,1/Q[F]+(r,1/F)+S(r,f)) 相似文献
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设(F)为定义在区域D内的一族亚纯函数,a(z)和b(z)为两个在D满足a(z)≠b(z)和a(z)≠b(k)(z)以及a(z)(≠)a'(z)的全纯函数,若对于任意的f∈(F),f(z)-a(z)的零点重级至少是k,f(z)和f(k)(z)分担a(z),且当f(z)=b(z)时,f(k)(z)=b(z),那么(F)在... 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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主要研究了具有四个分担值的亚纯函数的密指量的相对增长性,证明了对于C中的判别的非常数亚纯函数(fz),g(z),如果aj(j=1,2,3,4)为其判别的分担值,其中a4是其CM分担值,且■λ>2/3,ER+,mesE<+∞且(r,f)>λT(r,f)(r■E),则有(2/3+o(1))Σ(N(r,g=aj) j from 1 to 4)≤Σ(N(r,f=aj) j from 1 to 4)≤(2/3+o(1))Σ(N(r,g=aj) j from 1 to 4)(r■E;r→∞)。 相似文献
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文章研究了亚纯函数的唯一性,得到了关于亚纯函数f(z)和g(z)分担5个小函数的一个唯一性定理. 相似文献
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This paper presents an inequality, by use of which some results about the value distribution of f nf (k) are proved, where n and k are two positive integers. 相似文献
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HUANG Xiao-jie LAN Fu-xiang 《重庆大学学报(英文版)》2007,6(4):302-304
This paper presents an inequality, by use of which some results about the value distribution of f nf (k) are proved, where n and k are two positive integers. 相似文献
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