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1.
In this paper, using the concept ofA-statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation
theorem which concerns the problem of approximating a functionf by means of a sequenceL
n
f of positive linear operators. 相似文献
2.
Tülin Coşkun 《Proceedings Mathematical Sciences》2000,110(4):357-362
In this work we obtain, under suitable conditions, theorems of Korovkin type for spaces with different weight, composed of continuous functions defined on unbounded regions. These results can be seen as an extension of theorems by Gadjiev in [4] and [5]. 相似文献
3.
In this paper we develop the main aspects of the Bohman–Korovkin theorem on approximation of continuous functions with the use of A-statistical convergence and matrix summability method which includes both convergence and almost convergence. Since statistical convergence and almost convergence methods are incompatible we conclude that these methods can be used alternatively to get some approximation results. 相似文献
4.
Questions of approximative nature are considered for a space of functions L
p(G, ), 1 p , defined on a locally compact abelian Hausdorff group G with Haar measure . The approximating subspaces which are analogs of the space of exponential type entire functions are introduced. 相似文献
5.
Mehmet Ali Özarslan Hüseyin Aktuğlu 《Mathematical Methods in the Applied Sciences》2015,38(9):1937-1944
In this paper, we prove a certain Korovkin type approximation theorem by introducing new test functions. We introduce the non‐tensor Balázs type Bleimann, Butzer and Hahn operators and give the approximation property by using this new Korovkin theorem. Furthermore, we obtain the rate of convergence of these operators by means of modulus of continuity. Finally, we state the multivariate version of the abovementioned Korovkin type theorem. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
On the Rate of Convergence of Lp Norms in the Central Limit Theorem for Independent Random Variables
We present the upper and lower bounds of the L
p norms np of order n
-1 for all p, 1 p , in the central limit theorem for independent identically distributed random variables with the finite fourth and zero first and third moments of summands. The proof of the upper estimates of the norms np is based on a linear differential equation formed from the characteristic function of the sum of independent random variables. 相似文献
7.
Kairat T. Mynbaev 《Advances in Applied Mathematics》2001,26(4):302
The properties of L2-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of L2-approximable sequences since 1976 when Moussatat introduced a narrower notion of L2-generated sequences. The method relies on a study of certain linear operators in the spaces Lp and lp. A criterion of Lp-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method. 相似文献
8.
We present a short proof of the sharpness of the Calderón-Lozanovskii interpolation construction in couples of weighted L p spaces in the “lower triangle,” i.e., for operators from a couple { L p0 (V 0), L p1 (V 1)} to a couple {L q0 (U 0), L q1 (U 1)} with p 0 ? q 0 and p 1 ? q 1. This generalizes the well-known result due to Dmitriev and Semenov on the sharpness of the Riesz-Thorin interpolation theorem in the “lower triangle” for L p spaces on intervals. 相似文献
9.
J. Sunklodas 《Lithuanian Mathematical Journal》2009,49(2):216-221
In the paper, we present upper bounds of L
p
norms of order (
X)-1/2 for all 1 ≤ p ≤ ∞ in the central limit theorem for a standardized random variable (X−
X)/ √
X, where a random variable X is distributed by the Poisson distribution with parameter λ > 0 or by the standard gamma distribution Γ(α, 0, 1) with parameter
α > 0.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09. 相似文献
10.
Ogün Do?ru 《Journal of Mathematical Analysis and Applications》2008,342(1):161-170
In the present paper we introduce a generalization of positive linear operators and obtain its Korovkin type approximation properties. The rates of convergence of this generalization is also obtained by means of modulus of continuity and Lipschitz type maximal functions. The second purpose of this paper is to obtain weighted approximation properties for the generalization of positive linear operators defined in this paper. Also we obtain a differential equation so that the second moment of our operators is a particular solution of it. Lastly, some Voronovskaja type asymptotic formulas are obtained for Meyer-König and Zeller type and Bleimann, Butzer and Hahn type operators. 相似文献
11.
In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if : MNis a p-harmonic morphism (p2) from a complete noncompact Riemannian manifold Mof nonnegative Ricci curvature into a Riemannian manifold Nof nonpositive scalar curvature such that the p-energy E
p
(), or (2p–2)-energy E
2p–2() is finite, then is constant. 相似文献
12.
J. Sunklodas 《Lithuanian Mathematical Journal》2001,41(3):292-305
We derive lower bounds for Lp norms
, in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments. 相似文献
13.
Mats Boman 《BIT Numerical Mathematics》2006,46(2):249-260
We consider the orthogonal L2-projection P onto continuous finite element spaces. We prove estimates for P in a weighted Lp-norm and use these to prove corresponding approximation properties.
AMS subject classification (2000) 65N60, 35K85 相似文献
14.
ChangJian Zhao 《中国科学A辑(英文版)》2008,51(12):2172-2188
In this paper the author first introduce a new concept of L
p
-dual mixed volumes of star bodies which extends the classical dual mixed volumes. Moreover, we extend the notions of L
p
intersection body to L
p
-mixed intersection body. Inequalities for L
p
-dual mixed volumes of L
p
-mixed intersection bodies are established and the results established here provide new estimates for these type of inequalities.
This work was supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605065) and the Foundation
of the Education Department of Zhejiang Province of China (Grant No. 20050392) 相似文献
15.
Let p be a prime divisor of the order of a finite group G. Thompson (1970, J. Algebra14, 129–134) has proved the following remarkable result: a finite group G is p-nilpotent if the degrees of all its nonlinear irreducible characters are divisible by p (in fact, in that case G is solvable). In this note, we prove that a group G, having only one nonlinear irreducible character of p′-degree is a cyclic extension of Thompson's group. This result is a consequence of the following theorem: A nonabelian simple group possesses two nonlinear irreducible characters χ1 and χ2 of distinct degrees such that p does not divide χ1(1)χ2(1) (here p is arbitrary but fixed). Our proof depends on the classification of finite simple groups. Some properties of solvable groups possessing exactly two nonlinear irreducible characters of p′-degree are proved. Some open questions are posed. 相似文献
16.
17.
In this paper, we obtain that a strongly singular integral operator is bounded on
space for 1 < p < ∞. We also obtain that a strongly singular integral operator is a bounded operator from
to
for some weight w and 0 < p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on
for some w and 0 < p ≤ 1.
Supported by National 973 Program of China (Grant No. 19990751) 相似文献
18.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
19.
20.
We determine the L
p
discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the L
p
discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound
on L
p
discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the
Hammersley point set and show that there always exist permutations such that the L
p
discrepancy of the generalized Hammersley point set is of best possible order. For the L
2 discrepancy such permutations are given explicitly.
F.P. is supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research
Network “Analytic Combinatorics and Probabilistic Number Theory”. 相似文献