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单级零点较少的亚纯函数的一个界囿不等式 总被引:1,自引:0,他引:1
本文证明了:若.f(z)为复平面上的非线性亚纯函数,满足N1(r,1/f)=S(r,f),则对任何非零复数c,成立T(r,f)<11N(r,f)+11N(r,1/f'-c)+S(r,f).这里N1(r,1/f)表示f(z)的单级零点的计数函数. 相似文献
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By using small function method, the following result is obtained. If f(z) is transcendental meromorphic and that Ψ(z) is non-zero meromorphic and that T(r, Ψ) =S(r, f), then (n 1)T(r,f)≤(-N)(r,1/f'fn-Ψ) 2(-N)(r,1/f) (-N)(r,f) S(r,f). 相似文献
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Let f(z) be a meromorphic function andΨbe the differential polynomial of f which satisfies the condition of N(r, f) N (r, 1/f) = S(r, f). We obtain several results about the zero point of theΨand those results extend and improve the results of Yang and Yi in this paper. 相似文献
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关于亚纯函数及其导数的唯一性 总被引:7,自引:0,他引:7
1 引言和主要结果 设f(z)是复平面上的亚纯函数,T(r.f)、N(r,f)、m(r,f)、…等是值分布理论中通常的符号(参阅[8]),文章中T(r,a)=o(T(r,f))表示当r→∞时可能除去至多一有限测度集后成立。 设f(z)、g(z)为复平面上的亚纯函数,a为任意复数,我们说a 是f(z)和g(z)的分机位:如果f(z)-a与g(z)-a有相同的零点.特别称a是f(z)和g(z)的CM-分担值(Coun-ting Multiplicities):如果 f(z)-a与g(z)-a具有相同的零点,且重数相同;称a是f(z)和 相似文献
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1 引言及结果 设f是复平面C中超越亚纯函数.亚纯函数a_i(z)称为小函数,若a_i(z)满足T(r,a_i)=o(T(r,f))(i=1,2,…)。我们采用Nevanlinna理论中常用记号,用S(r,f)表示量:当f为有穷级时S(r,f)=O(log r);当f为无穷级时S(r,f)=O(log r T(r,f)),至多除去r的一个有限测度集。 相似文献
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In this paper we construct a new operator Hn,r(N,B) (f; z) by means of the partial sums S(N,S) (f; z) of Neumann-Bessel series. The operator converges uniformly to any fixed continuous function f(z) on the unit circle | z |= 1 and has the best approximation order for f(z) on | z |= 1. 相似文献
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亚纯函数F(z)称为复合,如果F(z)能分解为F(z)=f(f(z)), (1) 其中f是亚纯,g是整函数且f,g均非线性函数(当f是有理函数时,g可以是亚纯函数)。采用Nevanlinna理论的标准记号和结果,并引进记号△(a(z),f)=1-limijf r→∞N(r,a(z),f)/T(r,f), (2) 相似文献
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W.K.Hayman[1]于1959年建立了著名不等式:用亚纯函数f(z)的零点幂指量N(r,1/f)和它的某个导数f_((z))~((k))的1值点的幂指量N(r,1/f~((k))-1)去限制f(z)的特征函数。 顾永兴于1979年证明了相应的正规定则 相似文献
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首先对现行教材中初等函数的定义提出了商讨意见,讨论了高等数学教材中出现的形式上的非初等函数与初等函数的关系,并通过一些有代表性的例子加以说明. 相似文献
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In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc. 相似文献
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In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk. 相似文献
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In this paper,the characteristic function of the derivative of meromorphic func- tion is studied.A expression of characteristic function T(r,f~1)is given. 相似文献
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姚卫红 《数学物理学报(B辑英文版)》2003,23(1)
This paper proves a result that if two entire functions f(z) and g(z) share foursmall functions aj (z) (j = 1,2, 3, 4) in the sense of Ek) (aj, f) = Ek)(aj, g), (j = 1, 2, 3, 4)(k ≥ 11), then there exists f(z) = g(z). 相似文献
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ON ENTIRE FUNCTIONS, BLOCH AND NORMAL FUNCTIONS 总被引:1,自引:0,他引:1
New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function. 相似文献
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In this paper we derive certain suffcient conditions for starlikeness and con-vexity of orderαof meromorphically multivalent functions in the punctured unit disk. 相似文献
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姚卫红 《数学物理学报(B辑英文版)》2003,(1)
This paper proves a result that if two entire functions f(z) and g(z) share four small functions aj(z) (j = 1,2,3,4) in the sense of Ek)(aj, f) = Ek)(aj,g), (j = 1,2,3,4) (k ≥ 11), then there exists f(z) = g(z). 相似文献
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研究negabent函数之间的关系,并利用bent-negabent函数构造出代数次数达到次最优的semibent-negabent函数. 相似文献