共查询到20条相似文献,搜索用时 0 毫秒
1.
线性微分多项式的零点与极点 总被引:3,自引:0,他引:3
对Frank-Weissenborn不等式中导数f~((k))能否被替换成一般的线性微分多项式a_0f+a_1f′+…+a_kf~((k))进行了研究,并彻底解决了这一问题.作为此结果的应用,Hayman-Yang不等式等几个已有的定理也得到了推广.例子表明,本文所得到的几个不等式的条件是基本的. 相似文献
2.
单纯形上的Stancu多项式与最佳多项式逼近 总被引:8,自引:2,他引:6
作为Bernstein多项式的推广,本文定义单纯形上的多元Stancu多项式.以最佳多项式逼近为度量,建立Stancu多项式对连续函数的逼近定理与逼近阶估计,给出Stancu多项式的一个逼近逆定理,从而用最佳多项式逼近刻划Stancu多项式的逼近特征. 相似文献
3.
The value distribution of differential polynomials is studied.The re- suits in this paper improve and generalize some previous theorems given by Yang Chungchun(On deficiencies of differential polynomials,Math.Z.,116(1970),197- 204),H.S.Gopalakrishna and S.S.Bhoosnurmath(On distribution of values of differential polynomials,Indian J.Pure Appl.Math.,17(1986),367-372),I.Lahiri (A note on distribution of nonhomogeneous differential polynomials,Hokkaido Math. J.,31(2002),453-458)and Yi Hongxun(On zeros of differential polynomials,Adv. in Math.,18(1989),335-351)et al.Examples show that the results in this paper are sharp. 相似文献
4.
On Converse Theorem of Best Approximation by Polynomials in Bergman Spaces H_q~p(p>0,q>1) 总被引:1,自引:0,他引:1
A Bernstein type theorem and a converse theorem of best approximation by polynomials inBergman spaces H_q~p(p>0,q>1) are proved.Some proofs and results in [1] are in proved. 相似文献
5.
6.
对于具有等距分布插值结点的三角多项式,借助广义的Minkowski不等式在Orlicz空间内建立了由三角多项式逼近的渐近等式.并对于Orlicz空间内不同的函数类给出不同的结果. 相似文献
7.
Donal O'REGAN Naseer SHAHZAD 《数学学报(英文版)》2007,23(9):1601-1610
Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved. 相似文献
8.
9.
Lian Hai & Garidi Wu 《分析论及其应用》2013,29(2):149-157
In order to study the approximation by reciprocals of polynomials with real coefficients, one always assumes that the approximated function has a fixed sign on the given interval. Sometimes, the approximated function is permitted to have finite sign changes, such as $l(l\geq1)$ times. Zhou Songping has studied the case $l=1$ and $l\geq2$ in $L^{p}$ spaces in order of priority. In this paper, we studied the case $l\geq2$ in Orlicz spaces by using the function extend, modified Jackson kernel, Hardy-Littlewood maximal function, Cauchy-Schwarz inequality, and obtained the Jackson type estimation. 相似文献
10.
We use matrix inequalities to prove several bounds and majorization relations for the zeros of polynomials. Our results generalize the classic bound of Montel and improve some other known bounds. 相似文献
11.
In this article we consider the best polynomial approximation operator, defined in an Orlicz space L Φ(B), and its extension to L ?(B) where ? is the derivative function of Φ. A characterization of these operators and several properties are obtained. 相似文献
12.
针对典型教学案例,借助MATLAB的绘图与动画功能,通过编制程序并绘制图像,探讨Taylor多项式逼近函数的直观解释,以求帮助学生深入理解函数的Taylor展开式. 相似文献
13.
在赋Orlicz范数的Orlicz空间中,给出最佳逼近算子单调性的一个充分条件和最佳逼近元存在定理. 相似文献
14.
陶志雄 《数学年刊A辑(中文版)》2011,32(1):63-70
利用数论理论证明了纽结的Jones多项式仅有可能的有理根是O,而链环的Jones多项式仅有可能的有理根是0和-1.给出了作为Jones多项式根的所有可能单位根,以及所有可能的具有平凡Mahler测度的Jones多项式.最后指出了交叉数不超过11的纽结中,只有4_1,8_9,9_(42),K11n19的Jones多项式具有平凡的Mahler测度,从而回答了林晓松提出的关于Mahler测度的一个问题. 相似文献
15.
In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m~p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ. 相似文献
16.
本文在Bergman空间Bqp(p>0,q>1)中得到了关于用多项式逼近该空间函数的最佳逼近误差的阶的估计的逆定理. 相似文献
17.
本文在Bergman空间Bqp(p>0,q>1)中得到了关于用多项式逼近该空间函数的最佳逼近误差的阶的估计的逆定理. 相似文献
18.
Krawtchouk多项式在现代物理学中有着广泛应用.基于Li和Wong的结果,利用Airy函数改进了Krawtchouk多项式的渐近展开式,而且得到了一个一致有效的渐近展开式A·D2进一步,利用Airy函数零点的性质,推导出了Krawtchouk多项式零点的渐近展开式,并讨论了其相应的误差限.同时还给出了Krawtchouk多项式和其零点的渐近性态,它优于Li和Wong的结果. 相似文献
19.
Denote by xn,k(α,β) and xn,k(λ)=xn,k(λ−1/2,λ−1/2) the zeros, in decreasing order, of the Jacobi polynomial P(α,β)n(x) and of the ultraspherical (Gegenbauer) polynomial Cλn(x), respectively. The monotonicity of xn,k(α,β) as functions of α and β, α,β>−1, is investigated. Necessary conditions such that the zeros of P(a,b)n(x) are smaller (greater) than the zeros of P(α,β)n(x) are provided. A. Markov proved that xn,k(a,b)<xn,k(α,β) (xn,k(a,b)>xn,k(α,β)) for every n
and each k, 1kn if a>α and b<β (a<α and b>β). We prove the converse statement of Markov's theorem. The question of how large the function fn(λ) could be such that the products fn(λ)xn,k(λ), k=1,…,[n/2] are increasing functions of λ, for λ>−1/2, is also discussed. Elbert and Siafarikas proved that fn(λ)=(λ+(2n2+1)/(4n+2))1/2 obeys this property. We establish the sharpness of their result. 相似文献
20.
本文给出了基于Lascenov多项式零点(0,2)-插值正则性的充要条件,并给出基多项式存在时的明显表达式。 相似文献