On the order of approximation by modified summation-integral-type operators based on two parameters

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0182

S. A. Mohiuddine, Karunesh Singh, Abdullah Alotaibi

引用次数: 6

Abstract

Abstract In this article, we the study generalized family of positive linear operators based on two parameters, which are a broad family of many well-known linear positive operators, e.g., Baskakov-Durrmeyer, Baskakov-Szász, Szász-Beta, Lupaş-Beta, Lupaş-Szász, genuine Bernstein-Durrmeyer, and Pǎltǎnea. We first find direct estimates in terms of the second-order modulus of continuity, then we find an estimate of error in the Ditzian-Totik modulus of smoothness. Then we discuss the rate of approximation for functions in the Lipschitz class. Furthermore, we study the pointwise Grüss-Voronovskaja-type result and also establish the Grüss-Voronovskaja-type asymptotic formula in quantitative form.

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基于两参数的修正求和积分型算子的逼近阶

摘要在本文中，我们研究了基于两个参数的广义线性正算子族，这是许多著名线性正算子的广义族，例如Baskakov-Durrmeyer、Baskakov-SzáSz、Szásh-Beta、Lupaş-Beta，Lupaş-Szás z、真正的Bernstein Durrmeyer和Pāltīnea。我们首先找到了二阶连续模的直接估计，然后我们找到了Ditzian-Totik光滑模的误差估计。然后我们讨论了Lipschitz类函数的逼近率。此外，我们还研究了Grüss-Voronovskaja型逐点结果，并建立了Grúss-Vorovskaja类型的定量渐近公式。

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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.