共查询到20条相似文献,搜索用时 63 毫秒
1.
Borislav R. Draganov 《Numerical Functional Analysis & Optimization》2019,40(7):803-824
We characterize the approximation of functions in the Lp-norm by the Szász-Mirakjan-Kantorovich operator. We prove a direct and a strong converse inequality of type B in terms of an appropriate K-functional. 相似文献
2.
In the spaces L p on the line with power weight, we study approximation of functions by entire functions of exponential type. Using the Dunkl difference-differential operator and the Dunkl transform, we define the generalized shift operator, the modulus of smoothness, and the K-functional. We prove a direct and an inverse theorem of Jackson-Stechkin type and of Bernstein type. We establish the equivalence between the modulus of smoothness and the K-functional. 相似文献
3.
Biancamaria Della Vecchia Giuseppe Mastroianni Szabados J 《Acta Mathematica Hungarica》2006,111(4):325-345
Summary We give error estimates for the weighted approximation of functions with singularities at the endpoints on the semiaxis by
some modifications of Sz\'asz--Mirakyan operators. To do so, we define a new weighted modulus of smoothness and prove its
equivalence to the weighted K-functional. Also, the class of functions for which the modified Sz\'asz--Mirakyan operator can be defined will be extended
to a much wider set than for the original operator. 相似文献
4.
Some aspects of the interplay between approximation properties of analytic functions and the smoothness of its boundary values are discussed. One main result describes the equivalence of a special q-modulus of continuity and an intrinsic K-functional. Further, a generalization of a theorem due to G. H. Hardy and J. E. Littlewood (1932, Math. Z.34, 403–439) on the growth of fractional derivatives is deduced with the help of this K-functional. 相似文献
5.
Mieczysław Mastyło 《Potential Analysis》2011,35(4):301-328
We define a general variant of the modulus of smoothness in metric spaces and show that under mild condition it is equivalent
to the K-functional of a couple of Besov type spaces which in special cases coincide with spaces defined by Korevaar and Schoen. We
prove various symmetrization inequalities which involve the modulus, the K-functional and the isoperimetric estimators. We also characterize the Hajłasz-type Sobolev spaces defined not necessarily
on doubling measure spaces by means of generalized Poincaré inequalities. This require to study of some variants of the Fefferman–Stein
sharp functions as well as the Hardy–Littlewood maximal operators. 相似文献
6.
We prove that a sectorial operator admits an H
∞-functional calculus if and only if it has a functional model of Nagy–Foiaş type. Furthermore, we give a concrete formula
for the characteristic function (in a generalized sense) of such an operator. More generally, this approach applies to any
sectorial operator by passing to a different norm (the McIntosh square function norm). We also show that this quadratic norm
is close to the original one, in the sense that there is only a logarithmic gap between them. 相似文献
7.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1997,49(6):844-864
We establish upper bounds of the best approximations of elements of a Banach space B by the root vectors of an operator A that acts in B. The corresponding estimates of the best approximations are expressed in terms of a K-functional associated with the operator A. For the operator of differentiation with periodic boundary conditions, these estimates coincide with the classical Jackson inequalities for the best approximations of functions by trigonometric polynomials. In terms of K-functionals, we also prove the abstract Dini-Lipschitz criterion of convergence of partial sums of the decomposition of f from B in the root vectors of the operator A to f 相似文献
8.
We give a strong converse inequality of type B in terms of unified K-functional Kλα( f,t2)(0λ1, 0<α<2) for Baskakov operators. 相似文献
9.
We describe the K-functional and identify the real interpolated spaces of general quasi–Banach couples of classical Lorentz spaces. Applications are given which include interpolation of spaces of Lorentz–Zygmund type. 相似文献
10.
We study the L
p
-saturation for the linear combination of Bernstein-Kantorovich operators. As a result we obtain the saturation class by using
K-functional as well as some modulus of smoothness.
Research supported by National Natural Science Foundation of China (10671019) and Zhejiang Provincial Natural Science Foundation
of China (102005). 相似文献
11.
In this paper, we study multivariate Baskakov operator Bn,d(f,x). We first show that the operator can retain some properties of the original function f, such as monotony, semi-additivity and Lipschitz condition, etc. Secondly, we discuss the monotony on the sequence of multivariate Baskakov operator Bn,d(f,x) for n when the function f is convex. Then, we propose, for estimating the rate of approximation, a new modulus of smoothness and prove the modulus to be equivalent to certain K-functional. Finally, with the modulus of smoothness as metric, we establish a strong direct theorem by using a decomposition technique for the operator. 相似文献
12.
Honey Sharma 《分析论及其应用》2011,27(1):40-50
In this paper we introduce a generalization of Bernstein polynomials based on q calculus.With the help of Bohman-Korovkin type theorem,we obtain A-statistical approximation properties of these operators.Also,by using the Modulus of continuity and Lipschitz class,the statistical rate of convergence is established.We also gives the rate of A-statistical convergence by means of Peetre's type K-functional.At last,approximation properties of a rth order generalization of these operators is discussed. 相似文献
13.
14.
We consider the inflation class operator, denoted by F, where for any class K of algebras, F(K) is the class of all inflations of algebras in K. We study the interaction of this operator with the usual algebraic operators H, S andP, and describe the partially-ordered monoid generated by H, S, P andF (with the isomorphism operator I as an identity).
Received February 3, 2004; accepted in final form January 3, 2006. 相似文献
15.
Çiğdem Atakut 《Numerical Functional Analysis & Optimization》2016,37(12):1488-1502
In this article, we give a generalization of the Kantorovich-Szász type operators defined by means of the Brenke type polynomials introduced in the literature and obtain convergence properties of these operators by using Korovkin’s theorem. Some graphical examples using the Maple program for this approximation are given. We also establish the order of convergence by using modulus of smoothness and Peetre’s K-functional and give a Voronoskaja type theorem. In addition, we deal with the convergence of these operators in a weighted space. 相似文献
16.
Approximation by averages of the generalized translation induced by Laguerre and Jacobi expansions will be shown to satisfy
a strong converse inequality of type B with the appropriate K -functional.
April 9, 1998. Date revised: February 22, 1999. Date accepted: March 5, 1999. 相似文献
17.
Svante Janson 《Arkiv f?r Matematik》1993,31(2):307-338
We extend recent results by Pisier onK-subcouples, i.e. subcouples of an interpolation couple that preserve theK-functional (up to constants) and corresponding notions for quotient couples. Examples include interpolation (in the pointwise
sense) and a reinterpretation of the Adamyan-Arov-Krein theorem for Hankel operators.
This work was done at the Mittag-Leffler Institute. I am particularly grateful to Richard Rochberg for helpful discussions. 相似文献
18.
We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor
products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic
wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of periodic
functions [DPT].
October 16, 1995. Date revised: August 28, 1996. 相似文献
19.
Bruce Wood 《Journal of Approximation Theory》1978,23(4):354-363
The degree of Lp-approximation for a class of positive convolution operators is investigated. Recent results of De Vore, Bojanic, and Shisha for the uniform approximation by these operators and the K-functional of Peetre are employed to obtain the degree of approximation in terms of the integral modulus of smoothness. 相似文献
20.
Monia Giandomenico Adam N. Letchford Fabrizio Rossi Stefano Smriglio 《Mathematical Programming》2009,120(2):381-401
Although the lift-and-project operators of Lovász and Schrijver have been the subject of intense study, their M(K, K) operator has received little attention. We consider an application of this operator to the stable set problem. We begin
with an initial linear programming (LP) relaxation consisting of clique and non-negativity inequalities, and then apply the
operator to obtain a stronger extended LP relaxation. We discuss theoretical properties of the resulting relaxation, describe
the issues that must be overcome to obtain an effective practical implementation, and give extensive computational results.
Remarkably, the upper bounds obtained are sometimes stronger than those obtained with semidefinite programming techniques.
相似文献