共查询到18条相似文献,搜索用时 120 毫秒
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本文主要从收敛数列、函数连续性和函数单调性等几个方面讨论有界闭区间上的函数列一致收敛性的问题,得到或改进了函数列一致收敛的充分条件,并且给出每个结果的具体应用. 相似文献
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判别函数列一致收敛的方法有函数列一致收敛定义、Cauchy一致收敛准则、limn→∞supx∈D|fn(x)-f(x)|=0及Dini定理,本文由函数列的等度连续性,可得出几个有界闭区间上连续函数列一致收敛的充要条件,推广了Dini定理. 相似文献
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函数列的一致收敛性与所讨论的区间有关.在区间的子区间或不同的区间上,函数列的一致收敛性表现如何呢?通过几个命题和几个实例,并利用几何画板可以帮助我们辨别函数列在不同区间上的一致收敛性. 相似文献
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平均值函数列 总被引:1,自引:0,他引:1
经家麒 《数学的实践与认识》1998,(3)
本文用公理方法定义了平均值函数列.从公理定义出发,推证了平均值函数列的一系列共同性质,从而概括并推广了一些常见的平均值函数列.定理1指出了两个不同的平均值函数列的大小不会因变元的增加而改变,定理2揭示了平均值函数列与凸函数之间的内在联系,定理3则给出了多种平均值函数列的构作方法. 相似文献
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Let be an ideal of subsets of a metric space X,d. This paper considers a strengthening of the notion of uniform continuity of a function restricted to members of which reduces to ordinary continuity when consists of the finite subsets of X and agrees with uniform continuity on members of when is either the power set of X or the family of compact subsets of X. The paper also presents new function space topologies that are well suited to this strengthening. As a consequence of the general theory, we display necessary and sufficient conditions for continuity of the pointwise limit of a net of continuous functions. 相似文献
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就epi收敛性与其它一些收敛性的关系进行了研究,得出了epi收敛是函数收敛的弱化条件,并将epi收敛理论应用于优化问题. 相似文献
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Agata Caserta 《Journal of Mathematical Analysis and Applications》2010,371(1):384-775
In 1883 Arzelà (1983/1984) [2] gave a necessary and sufficient condition via quasi-uniform convergence for the pointwise limit of a sequence of real-valued continuous functions on a compact interval to be continuous. Arzelà's work paved the way for several outstanding papers. A milestone was the P.S. Alexandroff convergence introduced in 1948 to tackle the question for a sequence of continuous functions from a topological space (not necessarily compact) to a metric space. In 2009, in the realm of metric spaces, Beer and Levi (2009) [10] found another necessary and sufficient condition through the novel notion of strong uniform convergence on finite sets. We offer a direct proof of the equivalence of Arzelà, Alexandroff and Beer-Levi conditions. The proof reveals the internal gear of these important convergences and sheds more light on the problem. We also study the main properties of the topology of strong uniform convergence of functions on bornologies, initiated in Beer and Levi (2009) [10]. 相似文献
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首先介绍max-min复合意义下模糊矩阵幂序列的分解定理和周期指数定理.进一步,利用图论与分解定理讨论几种特殊的模糊矩阵在max-min复合意义下的周期指数和收敛指数. 相似文献
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Conjugate gradient optimization algorithms depend on the search directions.with different choices for the parameters in the search directions.In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved .Firstly,it is shown that,using reverse modulus of continuity funciton and forcing function,the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman‘s step size rule and a bounded level set .Secondly,by using comparing technique,some general convergence propecties of the new method with other kind of step size rule are established,Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method. 相似文献
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NA样本下回归函数估计的收敛速度 总被引:1,自引:0,他引:1
在误差为NA序列的条件下,研究了固定设计点列情形下非参数回归函数一般权函数的非参数估计,并在一些基本条件下给出了估计的一致最优强收敛速度. 相似文献