Quantitative Voronovskaya-type theorems for Fej\'er-Korovkin operators

IF 1.1 Q1 MATHEMATICS
J. Bustamante, Lázaro Flores De Jesús
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引用次数: 4

Abstract

In recent times quantitative Voronovskaya type theorems have been presented in spaces of non-periodic continuous functions. In this work we proved similar results but for Fejer-Korovkin trigonometric operators. That is we measure the rate of convergence in the associated Voronovskaya type theotem. Recall that these operators provide the optimal rate in approximation by positive linear operators. For the proofs we present new inequalities related with trigonometric polynomials as well as with the convergence factor of the Fej\'er-Korovkin operators. Our approach includes spaces of Lebesgue integrable functions.
Fej’er-Korovkin算子的定量Voronovskaya型定理
近年来,在非周期连续函数空间中提出了定量Voronovskaya型定理。在这项工作中,我们证明了类似的结果,但对于Fejer-Korovkin三角算子。也就是说,我们测量了相关Voronovskaya型系统的收敛速度。回想一下,这些算子在正线性算子的近似中提供了最优速率。对于证明,我们提出了与三角多项式以及Fej’er-Korovkin算子的收敛因子有关的新不等式。我们的方法包括勒贝格可积函数的空间。
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
Constructive Mathematical Analysis
Constructive Mathematical Analysis Mathematics-Analysis
CiteScore
2.40
自引率
0.00%
发文量
18
审稿时长
6 weeks
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