On the Best Quadrature Formula of Markov Type for Classes of Functions Defined by Moduli of Continuity

被引：0

作者：

Shabozov, M. Sh. ^{[1
]}

Shabozova, A. A. ^{[2
]}

机构：

[1] Acad Sci Republ Tajikistan, Inst Math, Dushanbe 734063, Tajikistan

[2] Tajik State Natl Univ, Dushanbe 734025, Tajikistan

来源：

VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS | 2024年 / 57卷 / 04期

关键词：

quadrature formula of Markov type; modulus of continuity; error;

D O I：

10.1134/S1063454124700419

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, for the specified classes of functions defined by moduli of continuity, the extremal problem of finding the best quadrature formula of Markov type is solved. It is proved that the best formula is the classical quadrature formula of trapezoids and its exact error estimate is calculated for the given class of functions. A similar fact is proved for classes of functions defined by the modulus of smoothness, as well as for intermediate classes of functions between the above-mentioned classes of functions defined by the moduli of continuity and moduli of smoothness.

引用

页码：555 / 561

页数：7

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