A characterization of the rate of approximation of Kantorovich sampling operators in variable exponent Lebesgue spaces

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作者：
Borislav R. Draganov
机构：
[1] Sofia University “St. Kliment Ohridski”,Department of Mathematics and Informatics
[2] Bulgarian Academy of Sciences,Institute of Mathematics and Informatics
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2024年 / 118卷
关键词：
Sampling operator; Kantorovich sampling operator; Direct estimate; Converse estimate; Modulus of smoothness; Variable exponent Lebesgue space; 41A17; 41A25; 41A27; 41A35; 41A40; 41A65;
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摘要：
We establish a direct and a matching two-term converse estimate by a K-functional and a modulus of smoothness for the rate of approximation by generalized Kantorovich sampling operators in variable exponent Lebesgue spaces. They yield the saturation property and class of these operators. We also prove a Voronovskaya-type estimate.
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