The Convergence of Some Positive Linear Operators on the Space of Multivariate Continuous Periodic Functions

被引：0

作者：

Popa, Dumitru ^{[1
]}

机构：

[1] Ovidius Univ Constanta, Dept Math, Bd Mamaia 124, Mamaia 900527, Constanta, Romania

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2024年 / 21卷 / 05期

关键词：

Korovkin approximation theorem; continuous 2 pi-periodic functions; test set of convergence; singular integral; approximation of multivariate periodic functions; rectangular method of summation; triangular method of summation;

D O I：

10.1007/s00009-024-02689-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

As a consequence of a general result, we prove that in the case of singular integrals the set of convergence consists only of the two functions 1 and cos. We prove also a multivariate version of this result and apply it to find the necessary and sufficient conditions for the convergence of the sequences of positive linear operators associated to the rectangular and triangular summation.

引用

页数：19

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