Approximation of classes of periodic multivariable functions by linear positive operators

被引：0

作者：

Bushev D.M. ^{[1
]}

Kharkevych Yu.I. ^{[1
]}

机构：

[1] Volyn University, Lutsk

来源：

Ukrainian Mathematical Journal | 2006年 / 58卷 / 1期

关键词：

Linear Operator; Dimensional Space; Periodic Function; Positive Operator; Linear Positive Operator;

D O I：

10.1007/s11253-006-0048-y

中图分类号：

学科分类号：

摘要：

In an N-dimensional space, we consider the approximation of classes of translation-invariant periodic functions by a linear operator whose kernel is the product of two kernels one of which is positive. We establish that the least upper bound of this approximation does not exceed the sum of properly chosen least upper bounds in m-and ((N - m))-dimensional spaces. We also consider the cases where the inequality obtained turns into the equality. © 2006 Springer Science+Business Media, Inc.

引用

页码：12 / 21

页数：9

共 4 条

[1] Zaderei P.V., On the approximation of periodic multivariable functions by positive polynomial operators, Studies on the Theory of Approximation of Functions and Applications [in Russian], (1978)
[2] Besov O.V., Ll'in V.T., Nikol'sldi S.M., Integral Representations of Functions and Imbedding Theorems [in Russian], (1975)
[3] Timan A.F., Theory of Approximation of Functions of Real Variables [in Russian], (1960)
[4] Stepanets A.I., Uniform Approximation by Trigonometric Polynomials [in Russian], (1981)

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