A note on the remainder in the approximation of functions by some positive linear operators

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2023-10-06 DOI:10.1007/s11117-023-01014-3

Marius-Mihai Birou

引用次数: 0

Abstract

Abstract In this note we give representations for the remainder in approximations formulas generated by positive linear operators which preserve some functions including linear functions. We show that in these cases the Peano kernel from the integral representation of the remainder has the same sign on the definition domain. Applications to the iterates of some positive linear operators and quadrature formulas are given.

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关于用某些正线性算子逼近函数的余数的注记

摘要本文给出了由正线性算子生成的近似公式中余数的表示，该近似公式保留了一些函数，包括线性函数。我们证明在这些情况下，由余数的积分表示得到的Peano核在定义定义域上具有相同的符号。给出了若干正线性算子和正交公式在迭代中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.