用 Szász-Mirakjan-Kantorovich 算子对函数进行加权逼近的强反演不等式

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-04-30 DOI:10.1007/s00025-024-02179-3

Ivan Gadjev, Parvan E. Parvanov, Rumen Uluchev

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引用次数: 0

摘要

我们研究了经典 Szász-Mirakjan 算子的 Kantorovich 修正在 \(L_p\)-norm 中对函数的加权逼近，其权重类型为 \((1+x)^{\alpha }\), \(\alpha \in {\mathbb {R}}\).通过使用适当的 K 函数，我们证明了加权近似误差的强反向不等式，并准确地描述了它的特征。我们证明了 Szász-Mirakjan-Kantorovich 算子的 Voronovskaya 和 Bernstein 型不等式。

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Strong Converse Inequality for Weighted Approximation of Functions by the Szász–Mirakjan–Kantorovich Operator

We investigate the weighted approximation of functions in \(L_p\)-norm by Kantorovich modifications of the classical Szász-Mirakjan operator, with weights of type \((1+x)^{\alpha }\), \(\alpha \in {\mathbb {R}}\). By using an appropriate K-functional we prove a strong converse inequality for the weighted error of approximation and characterize it exactly. We prove a Voronovskaya and Bernstein-type inequalities for the Szász-Mirakjan–Kantorovich operator.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.