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1.
Two Convergence Problems for Monotone Sequences 总被引:1,自引:0,他引:1
Eight measures of rate of convergence of monotone sequences of real numbers have been proposed and discussed in a paper by Beyer, Ebanks, and Qualls (Acta Appl. Math. 20 (1990), 267–284). These rates arose in discussions of dynamical systems. In the comparisons of these rates, two problems remained. A complete answer is given to one of the problems and a partial answer is given to the other problem. 相似文献
2.
XiuNaihua 《高校应用数学学报(英文版)》2000,15(4):433-442
In this paper, the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints ,and a SQP algorithm for this reformulation based on a damped Gauss-Newton type method is presented. It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity. 相似文献
3.
In this article we first give a characterisation of compact spaces among spaces by improving a theorem of J. Ewert. Then, with the aid of a new type of convergence, we give a characterisation of the pseudocompact and of the Lindelöf spaces.
4.
We prove a characterization showing when the ideal pointwise convergence does not imply the ideal equal (aka quasi-normal) convergence. The characterization is expressed in terms of a cardinal coefficient related to the bounding number b. We also prove a characterization showing when the ideal equal limit is unique. 相似文献
5.
It is shown that no notion of set convergence at least as strong as Wijsman convergence but not as strong as slice convergence can be preserved in superspaces. We also show that such intermediate notions of convergence do not always admit representations analogous to those given by Attouch and Beer for slice convergence, and provide a valid reformulation. Some connections between bornologies and the relationships between certain gap convergences for nonconvex sets are also observed.Research supported in part by an NSERC research grant and by the Shrum endowment.NSERC postdoctoral fellow. 相似文献
6.
In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical
convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations
between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions,
lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin type approximation
theorem via lacunary equi-statistical convergence is proved. Moreover it is shown that our Korovkin type approximation theorem
is a non-trivial extension of some well-known Korovkin type approximation theorems. Finally the rates of lacunary equi-statistical
convergence by the help of modulus of continuity of positive linear operators are studied.
相似文献
7.
J. E. Marcos 《Czechoslovak Mathematical Journal》2003,53(3):689-706
We define various ring sequential convergences on
and
. We describe their properties and properties of their convergence completions. In particular, we define a convergence
on
by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields
Further, we show that
is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan. 相似文献
8.
Two kinds of convergent sequences on the real vector space m of all bounded sequences in a real normed space X were discussed in this paper, and we prove that they are equivalent, which improved the results of [1]. 相似文献
9.
A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions
is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential
links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to
a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset
of all continuous functions is also addressed.
相似文献
10.
给出交错级数敛散性微分形式的判别法,应用此判别法可直接判别交错级数是否收敛,以及收敛时是绝对收敛还是条件收敛. 相似文献
11.
定义了单调收敛函数和交错收敛函数,并根据其收敛特点,提出并证明了加快其收敛速度的两个命题.算例表明其效果较好. 相似文献
12.
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
13.
Let I 2N be an ideal and let XI = span{χI : I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to pI-kernel convergence. In addition, let K = {x*oχ(·) : x*∈ p(e)}, where p(x) = lim supn→∞1/n(∑k=1n|x(k)|, and let Iμ = {A N : μ(A) = 0} for all μ = x*oχ(·) ∈ K. Then Iμ is a proper ideal. We also show that the ideal convergence deduced by the proper ideal Iμ, the p-kernel convergence and the statistical convergence are also equivalent. 相似文献
14.
研究了Banach空间Xμ={c=(ci)i≥1:||c||μ====def (^∞∑i=1)iμ|ci|∞},μ≥1,讨论了它的范数,紧性以及强收敛和弱收敛之间的关系. 相似文献
15.
Alternative Approaches to the Two-Scale Convergence 总被引:1,自引:1,他引:0
Luděk Nechvátal 《Applications of Mathematics》2004,49(2):97-110
Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions (x, y). Properties and examples are added. 相似文献
16.
Given convergent sequences of functions (f
n
) and (g
n
), we look for conditions ensuring that the sequences (f
n
+g
n
), (max(f
n
,g
n
)) and (f
n
g
n
) converge, being the infimal convolution. The convergences we use are variational convergences. This study is motivated by applications to Hamilton–Jacobi equations. 相似文献
17.
Jonathan M. Borwein Jon D. Vanderwerff 《Transactions of the American Mathematical Society》1996,348(4):1617-1631
We examine when a sequence of lsc convex functions on a Banach space converges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlevé-Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions. For example, a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of .
18.
M. C. Listán-García F. Rambla-Barreno 《Numerical Functional Analysis & Optimization》2013,34(11):1166-1174
We characterize uniform rotundity in every direction by means of rough convergence. This characterization still holds if we shift to rough statistical convergence. We also study the latter convergence in normed spaces. 相似文献
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