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1.
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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J. Ewert 《Periodica Mathematica Hungarica》1993,26(1):77-84
The almost uniform convergence is between uniform and quasi-uniform one. We give some necessary and sufficient conditions under which the almost uniform convergence coincides on compact sets with uniform, quasi-uniform or uniform convergence, respectively. In the second section continuity of almost uniform limits is considered. Finally we characterize the set of all points at which a net of functions is almost uniformly convergent to a given function. 相似文献
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Antonio Aizpuru Marina Nicasio-Llach 《Bulletin of the Brazilian Mathematical Society》2008,39(2):173-182
In this work we study the concept of statistical uniform convergence. We generalize some results of uniform convergence in
double sequences to the case of statistical convergence. We also prove a basic matrix theorem with statistical convergence. 相似文献
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At time tk, a unit with magnitude Xk and lifetime Lk enters a system. Let λ be a real valued function on the finite real sequences. One such sequence, B*t, consists of the Xk's for which tk t < tk + Lk. When λ(X1,…, Xn) converges (in some sense) to φ, we find conditions under which λ(B*t) converges or fails to converge to φ in the same sense. 相似文献
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A. Cellina F. Monti M. Spadoni 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(7):1966-1970
We consider a time optimal problem for a system described by a differential inclusion, whose right hand side is not necessarily convex valued. Under the assumption of strict convexity of the map obtained by convexifying the original, non-convex valued map, we obtain the strong convergence of the derivatives of any uniformly converging minimizing sequence. The assumptions required by this result are satisfied, for instance, by the classical brachystochrone problem and by Fermat’s principle. 相似文献
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A. Yu. Trynin 《Russian Mathematics (Iz VUZ)》2008,52(6):58-69
In this paper we obtain a criterion for the uniform convergence inside the interval (0, π) of values of E. T. Whittaker operators for continuous functions. This criterion is similar to that of A. A. Privalov for the convergence of interpolation Lagrange-Chebyshev polynomials and trigonometric ones.
相似文献
$L_n (f,x) = \sum\limits_{k = 0}^n {\frac{{sin(nx - k\pi )}}{{nx - k\pi }}f\left( {\frac{{k\pi }}{n}} \right)} $
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For sequences of the positively associated random variables which are strictly weaker than the classical associated random ones introduced by Esary et al. (1967) [7], strong convergence rate is obtained, which reaches the available one for independent random variables in terms of Berstein type inequality. Further, we give the corresponding precise asymptotics with respect to the rate mentioned above, which extend and improve the relevant results in Fu (2009) [8]. 相似文献
10.
Let {X
n
; n ≥ 1} be a sequence of independent and identically distributed U[0,1]-distributed random variables. Define the uniform empirical process $F_n (t) = n^{ - \tfrac{1}
{2}} \sum\nolimits_{i = 1}^n {(I_{\{ X_i \leqslant t\} } - t),0} \leqslant t \leqslant 1,\left\| {F_n } \right\| = \sup _{0 \leqslant t \leqslant 1} \left| {F_n (t)} \right|
$F_n (t) = n^{ - \tfrac{1}
{2}} \sum\nolimits_{i = 1}^n {(I_{\{ X_i \leqslant t\} } - t),0} \leqslant t \leqslant 1,\left\| {F_n } \right\| = \sup _{0 \leqslant t \leqslant 1} \left| {F_n (t)} \right|
. In this paper, the exact convergence rates of a general law of weighted infinite series of E {‖F
n
‖ − ɛg
s
(n)}+ are obtained. 相似文献
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On the uniform convergence of the Fourier series for one spectral problem with a spectral parameter in a boundary condition 下载免费PDF全文
In this paper, we investigate the uniform convergence of the Fourier series expansions in terms of eigenfunctions for the spectral problem where λ is a spectral parameter, q(x) is a real‐valued continuous function on the interval [0,1], and a1,b0,b1,c1,d0, and d1 are real constants that satisfy the conditions Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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R.S Singh 《Journal of multivariate analysis》1979,9(1):157-164
Based on a random sample from a population with (unknown) probability density f, this note exhibits a class of statistics f(p) for each fixed integer . It is shown that f(p) are uniformly strongly consistent estimators of f(p), the pth order derivative of f, if and only iff(p)is bounded and uniformly continuous. 相似文献
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Luminia Simona Vî 《Mathematical Logic Quarterly》2003,49(3):255-259
The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity. 相似文献
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Behzad Djafari Rouhani Hadi Khatibzadeh 《Journal of Mathematical Analysis and Applications》2010,363(2):648-654
In this paper, we establish the strong convergence of possible solutions to the following nonhomogeneous second order evolution system
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A note on the rate of convergence in the strong law of large numbers for martingales 总被引:1,自引:0,他引:1
George Stoica 《Journal of Mathematical Analysis and Applications》2011,381(2):910-913
We prove a Baum-Katz-Nagaev type rate of convergence in the Marcinkiewicz-Zygmund and Kolmogorov strong laws of large numbers for norm bounded martingale difference sequences. 相似文献
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A. Aizpuru F.J. Pérez-Fernández 《Journal of Mathematical Analysis and Applications》2003,284(1):89-96
Several classical results on uniform convergence of unconditionally Cauchy series are generalized to weakly unconditionally Cauchy series. This uniform convergence is characterized through subalgebras and subfamilies of . A generalization of the Orlicz-Pettis theorem is also proved by mean of subalgebras of . 相似文献