Approximation properties of the Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Mathematical Inequalities Pub Date : 2022-01-01 DOI:10.7153/jmi-2022-16-86

Nazim Mahhmudov, M. Kara

引用次数: 1

Abstract

. In the present paper, we introduce the Riemann-Liouville fractional integral type Sz´asz- Mirakyan-Kantorovich operators. We investigate the order of convergence by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre’s K-functional. Weigh- ted approximation properties of these operators in terms of modulus of continuity have been dis-cussed. Then, Vorononskaja-type type theorem are obtained. Moreover, bivariate the Riemann- Liouville fractional integral type Sz´asz-Mirakyan-Kantorovich operators are constructed. The last section is devoted to graphical representation and numerical results for these operators.

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Riemann-Liouville分数积分型Szász-Mirakyan-Kantorovich算子的近似性质

。本文引入了Riemann-Liouville分数阶积分型Sz´asz- Mirakyan-Kantorovich算子。利用lipschitz型极大函数、二阶光滑模和Peetre的k泛函研究了收敛的阶数。讨论了这些算子在连续模方面的加权逼近性质。然后，得到了vorononskaja型型定理。此外，构造了二元Riemann- Liouville分数积分型Sz´asz-Mirakyan-Kantorovich算子。最后一节专门讨论这些运算符的图形表示和数值结果。

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

Journal of Mathematical Inequalities MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.90

自引率

3.40%

发文量

审稿时长

6-12 weeks

期刊介绍： The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts. ''JMI'' is published quarterly; in March, June, September, and December.