Abstract Korovkin-type theorems in the filter setting with respect to relative uniform convergence

被引：3

作者：

Boccuto, Antonio ^{[1
]}

Demirci, Kamil ^{[2
]}

Yildiz, Sevda ^{[2
]}

机构：

[1] Univ Perugia, Dept Math & Comp Sci, Perugia, Italy

[2] Sinop Univ, Dept Math, Sinop, Turkey

来源：

TURKISH JOURNAL OF MATHEMATICS | 2020年 / 44卷 / 04期

关键词：

Korovkin theorem; relative uniform convergence; bivariate Kantorovich operator; LINEAR INTEGRAL-OPERATORS; NEURAL-NETWORK OPERATORS; APPROXIMATION THEOREMS; SPACES; SEQUENCES; FAMILY;

D O I：

10.3906/mat-1912-14

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point, belonging to the domain of the involved functions. We give some examples, in which we show that our results are strict generalizations of the classical ones.

引用

页码：1238 / 1249

页数：12

共 28 条

[21] Abstract Theorems on Exchange of Limits and Preservation of (Semi)continuity of Functions and Measures in the Filter Convergence Setting
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JOURNAL OF FUNCTION SPACES, 2016, 2016
[22] Deferred Cesaro and deferred Euler equi-statistical convergence and its applications to Korovkin-type approximation theorem
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[26] Approximation via statistical relative uniform convergence of sequences of functions at a point with respect to power series method
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[28] Statistical Relative A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document}-Summation Process and Korovkin-Type Approximation Theorem on Modular Spaces
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