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1.
关于单调函数的不动点问题   总被引:3,自引:0,他引:3  
关于单调函数的不动点问题王良成(四川省达县师专635000)本文用数学分析中的实数理论对一类未必连续的单调函数的不动点及其性质作如下探讨.定理1设f(x)为闭区间[a,b]上的单调增加函数,且,则f(x)在[a,b]上存在不动点.证国f(x)在[a,...  相似文献   

2.
热弹性理论准静态问题解的一般公式及其应用   总被引:2,自引:0,他引:2  
赵永安 《应用数学》1996,9(2):153-157
本文利用分解定理[1]求得热弹性理论的准静态问题在无限空间中的Green函数组.从而,借助于文[2]中的互易定理建立了该问题解的一般公式.  相似文献   

3.
n维复形上一类具有线性分式目标函数的规划问题郑汉鼎(山东大学教学系,济南2501O0)文献[1,2]已经研究了n维复形上的规划问题,本文将讨论。维复形上具有线性分式目标函数的规划问题.问题Ⅰ给定一个n维复形Kn和一个r-1维边缘链,要找一个r维链。使...  相似文献   

4.
一个初等对称函数不等式的加强   总被引:3,自引:1,他引:2  
汤子赓 《数学通报》1997,(10):44-46
一个初等对称函数不等式的加强汤子赓(浙江省绍兴市经济管理干部培训中心312000)本文对文[1]给出的关于初等对称函数的一个不等式,通过求得函数的下确解,得到最佳结果.为便于阅读,先将[1]中的有关概念介绍如下:n个正数x1,x2,…,xn的初等对称...  相似文献   

5.
关于求多元对称函数极值的一个磨光法   总被引:3,自引:0,他引:3  
赵德钧 《数学通报》1998,(12):31-32
文[1]给出了求三元对称函数最值的一个磨光法,本文将之推广到n元对称连续函数的情形.一个对称集合[2]D同时又是凸的,则称之为对称凸域.当Rn中的超平面ni=1xi=m上的点集D是对称凸的,则称D为超平面ni=1xi=m上的对称凸域(其中m为常数...  相似文献   

6.
本文在[1],[2]的基础上,给出了满足gn(x)=Cofn(x)+C1fn-1(x)+…+Ckfn-k(x)的相关函数序列{fn(x)}和{gn(x)}的极限间制约关系的一个命题,从而得到一种判断函数序列一致收敛并且求其极限函数的方法。  相似文献   

7.
高维空间的拟正则映照   总被引:1,自引:0,他引:1  
1引言 众所周知,设Ω是一个复平面区域,则中的Beltrami方程:的解w=f(z)称为上的 正则函数,当w=f(z)是同胚的时候,称为 共形映照.正则函数和什共形映照在复分析中有重要的理论意义和广泛的应用,并已被深入系统的研究[1-5].如何将它们推广到高维长期受到人们的关注,并已有了一些重要的工作.最近T.Iwaniec和G.Martin得到了Beltrami方程和正则函数的正则性理论在偶数维空间中的相应推广,这是拟正则函数的正则性理论研究中的一个重要发展[6];之后T.Iwaniec应用变…  相似文献   

8.
近于凸函数族的Fekete-Szegǒ问题   总被引:1,自引:0,他引:1  
设S为熟知的单位圆盘内的规范化单叶函数族.Fekete-Szego证明了众所周知的结果最近W.Koepf考虑了近于凸函数族K中的相应问题。得到了准确结果[1].本文讨论了β型近于凸函数族K(β)中的Fekete-Szego问题,也得到了准确结果,从而推广了文[1]中的结果.  相似文献   

9.
关于凸函数的一个控制不等式   总被引:4,自引:0,他引:4  
关于凸函数的一个控制不等式续铁权(青岛教育学院数学系266071)设f(x)在[a,b]上定义,0<t<1,若称f(x)是[a,b]上的凸函数,若当时严格不等式成立,称f(x)是严格凸函数.若不等式反向,称f(x)是凹函数和严格凹函数.本文研究凸函数...  相似文献   

10.
再论分式线性函数的迭代   总被引:2,自引:1,他引:1  
再论分式线性函数的迭代王浚岭(湖北三峡学院师范学院443000)1引言近年来,有一系列文章[1—7]讨论分式线性函数的迭代问题,给出了不少好的结果,但其中也有不少疏漏甚至是错误,主要表现在如下两个方面:第一,[4,5]给出的实函数f(x)=ax+bx...  相似文献   

11.
宁伟  杨德运 《应用数学》2001,14(4):78-81
本文给出的定理既适合于一维与高维,又适合于有噪与无噪的频变有限函数的外推,是对Sanz-Huang两个猜想的改进,同时讨论了外推数与真函数的逼近关系。  相似文献   

12.
Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.  相似文献   

13.
Neville extrapolation is generalized to expansions for which the extrapolation coefficients, used in the calculation of the elements in the related extrapolation table, are not known. It is proved that the extrapolation coefficients are the multipliers of a special Gaussian elimination process. The stability of the generalized extrapolation process is discussed. Application of generalized Neville extrapolation to integrals with weight functions/singularities in one or more dimensions is indicated.  相似文献   

14.
When the finite-difference method is used to solve initial- or boundary value problems with smooth data functions, the accuracy of the numerical results may be considerably improved by acceleration techniques like Richardson extrapolation. However, the success of such a technique is doubtful in cases were the right-hand side or the coefficients of the equation are not sufficiently smooth, because the validity of an asymptotic error expansion — which is the theoretical prerequisite for the convergence analysis of the Richardson extrapolation — is not a priori obvious. In this work we show that the Richardson extrapolation may be successfully applied to the finite-difference solutions of boundary value problems for ordinary second-order linear differential equations with a nonregular right-hand side. We present some numerical results confirming our conclusions.  相似文献   

15.
A method for exactly calculating norm on the sum of the cones of nonincreasing or concave functions in Lorentz spaces is proposed. The obtained result makes it possible to prove new extrapolation theorems for cones in Lorentz, Lebesgue, and Marcinkiewicz spaces with exact constants.  相似文献   

16.
周性伟  夏香根 《计算数学》1989,11(2):205-211
若已知整函数f(z)在一个具有聚点z_0的无限集D上的值,则从理论上说,可由估计f(z)在z_0的各阶导数再对f(z)在该点展成幂级数来计算f在D以外点处的值.很明显,这种过程在实际计算中是不可取的.此时的可计算性,是指对任何z?D及ε>0,  相似文献   

17.
Summary A numerical method is developed which handles the Bessel transform of functions having slow rates of decrease. The method replaces the Bessel transform by a related damped transform for which the sinc quadrature rule provides an efficient and accurate approximation. It is then shown that the value of the original Bessel transform can be obtained from the damped transform by extrapolation with the Thiele algorithm.  相似文献   

18.
It is shown that the calculation of the sum of the spaces of the K‐Peetre interpolation method can be reduced to the calculation of the sum of the cones of the concave functions included by the parameter in the definition of the spaces of the K‐Peetre interpolation method. As an example, a new extrapolation theorem for operators in Lipschitz spaces is obtained.  相似文献   

19.
The author has proposed a new approach to extrapolation of operators from the scale of Lebesgue spaces to the Orlicz spaces beyond this scale. In this article comprising two parts we develop some mathematical method that enables us to prove extrapolation theorems for arbitrary behavior of an operator in the Lebesgue scale (i.e., in the case when the norm of the operator is an arbitrary function of p) and also in the case when the basic scale is an interval of the Lebesgue scale with exponents separated from 1 or +∞. In this event, we face ill-posed problems of inversion of the classical Mellin and Laplace type integral transforms over nonanalytic functions in terms of their asymptotic behavior on the real axis and also the question about the properties of convolution type integral transforms on classes of N-functions. In the first part of the article we study integral representations for N-functions by expansions in power functions with a positive weight and the behavior of convolution type integral transforms on classes of N-functions.  相似文献   

20.
Summary An integral form of the remainder terms of the entries in the extrapolation scheme is shown to have kernels of constant sign within columns. Monotonicity of one or more derivatives of the function to be differentiated is transformed into certain monotonicity properties of the scheme. For functions of this kind the extrapolation scheme also provides for strict inclusions off(n) (0). This property may be extended to a larger class of functions through a majorant concept.  相似文献   

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