共查询到18条相似文献,搜索用时 62 毫秒
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本文考虑了非线性微分—差分方程fn(z)+q(z)eQ(z)f(k)(z+c)=p1eα1z+p2eα2z与fn(z)+q(z)eQ(z)△cf=p1eλz+p2e-λz解的增长性,其中n≥1,k≥1是两个整数,q(z)是非零多项式,Q(z)是非常数多项式.c,λ,α1,α2,p1,p2为非零常数,α1≠α2.特别地,... 相似文献
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研究了差分多项式H(z)=POk∑(i=1)a_if(z+c_i)的值分布,其中f是有限级超越整函数,P(f)是,的多项式,κ≥2,ci(i=1,…,k)是互不相同的常数,α_i(i=1,…,κ)是非零常数.得到了H(z)-a和H(z)-α(z)的零点的个数的估计,其中a∈C且α(z)(■0)为小函数.讨论了H(z)的非零有限Borel例外值的不存在性. 相似文献
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设f是一个有穷级的超越整函数,a,b,c是3个有穷复数,满足c≠0,a≠b,且n为正整数.如果a是f的Borel例外值,且Δ_c~nf(z)与f(z)IM分担b,则f(z)=a+Ae~(Bz),其中A,B为两个非零常数. 相似文献
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作者研究了有限级超越整函数的差分多项式和微-差分多项式的零点分布,在一定条件下得到了这些多项式的零点收敛指数的精确估计.所得结果可视为Hayman关于Picard例外值的经典结果的(微-)差分模拟. 相似文献
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研究了整函数及其差分多项式分担有限复数集的唯一性,得到了如下结果:设S_m={1,ω,…,ω~(m-1)},其中ω=cos(2π/m)+i sin(2π/m),c为非零有限复数,n(>5),m(≥2)均为正整数.如果f(z),g(z)为有限级整函数,满足E(S_m,f(z)~n(f(z)-1)f(z+c))=E(S_m,g(z)~n(g(z)-1))g(z+c)),那么f(z)≡g(z). 相似文献
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具有四个有穷的IM公共小函数的整函数 总被引:6,自引:0,他引:6
本文证明了两个非常数整函数若具有四个有穷的IM公共小函数,则它们必恒等.从而在整函数的情形下,Nevanlinna五值定理中的五个IM公共值能否更换为五个IM公共小函数(含∞)的问题的回答是肯定的. 相似文献
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王鸿 《纯粹数学与应用数学》2001,17(3):242-245
证明了线性微分多项式的一个基本定理,建立了线性微分多项式对有穷值的亏量关系,这些结果是对杨乐的两个定理的推广,例子表明,本文中定理的条件是必要的。 相似文献
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A. V. Olesov 《Journal of Mathematical Sciences》2006,133(6):1704-1717
The extremal properties of polynomials and entire functions of finite degree not vanishing in the upper half-plane are studied.
The exact inequalities obtained complement and strengthen the results by Genchev, Gardner and Govil, Turan, and Lax. Proofs
are based on a univalence condition established by Dubinin. Bibliography: 15 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 174–195. 相似文献
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We obtain new asymptotic relations for entire functions of finite order with zeros on a ray under the condition of regular growth for the counting function of their zeros. These relations improve the well-known results of Valiron. 相似文献
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This paper deals with some uniqueness problems of entire functions concerning differential polynomials that share one value with finite weight in a different form. We obtain some theorems which generalize some results given by Banerjee, Fang and Hua, Zhang and Lin, Zhang, etc. 相似文献
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We study a uniqueness question of entire functions sharing an entire function of smaller order with their diference operators,and deal with a question posed by Liu and Yang.The results in this paper extend the corresponding results obtained by Liu–Yang and by Liu–Laine respectively.Examples are provided to show that the results in this paper,in a sense,are the best possible. 相似文献
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Kai Liu 《Results in Mathematics》2010,57(3-4):365-376
This research is a continuation of a recent paper, due to Liu and Laine, dealing with difference polynomials of entire function. In this paper, we investigate the value distribution of difference polynomials of meromorphic functions and prove some difference analogues to some classical results for differential polynomials. 相似文献
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Ukrainian Mathematical Journal - We present a brief survey of works in the approximation theory of functions known to the author and connected with V. K. Dzyadyk’s research works. 相似文献