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Volume 40, Issue 3
Direct, Inverse Theorems of Approximation by Linear Combinations of Weighted Baskakov–Durrmeyer Operators in Orlicz Spaces

Lingxiong Han & Yumei Bai

DOI: 10.4208/ata.OA-2022-0013

Anal. Theory Appl., 40 (2024), pp. 221-239.

Published online: 2024-10

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  • Abstract

In the paper, the authors introduce the Orlicz space corresponding to the Young function and, by virtue of the equivalent theorem between the modified $K$-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems for the linear combinations of Jacobi weighted Baskakov–Durrmeyer operators in the Orlicz spaces.

  • Keywords

Direct theorem, inverse theorem, equivalent theorem, approximation, $K$-functional, Orlicz space, Jacobi weight, Baskakov–Durrmeyer operator.

  • AMS Subject Headings

41A17, 41A27, 41A35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-40-221, author = {Han , Lingxiong and Bai , Yumei}, title = {Direct, Inverse Theorems of Approximation by Linear Combinations of Weighted Baskakov–Durrmeyer Operators in Orlicz Spaces}, journal = {Analysis in Theory and Applications}, year = {2024}, volume = {40}, number = {3}, pages = {221--239}, abstract = {

In the paper, the authors introduce the Orlicz space corresponding to the Young function and, by virtue of the equivalent theorem between the modified $K$-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems for the linear combinations of Jacobi weighted Baskakov–Durrmeyer operators in the Orlicz spaces.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2022-0013}, url = {http://global-sci.org/intro/article_detail/ata/23466.html} }
TY - JOUR T1 - Direct, Inverse Theorems of Approximation by Linear Combinations of Weighted Baskakov–Durrmeyer Operators in Orlicz Spaces AU - Han , Lingxiong AU - Bai , Yumei JO - Analysis in Theory and Applications VL - 3 SP - 221 EP - 239 PY - 2024 DA - 2024/10 SN - 40 DO - http://doi.org/10.4208/ata.OA-2022-0013 UR - https://global-sci.org/intro/article_detail/ata/23466.html KW - Direct theorem, inverse theorem, equivalent theorem, approximation, $K$-functional, Orlicz space, Jacobi weight, Baskakov–Durrmeyer operator. AB -

In the paper, the authors introduce the Orlicz space corresponding to the Young function and, by virtue of the equivalent theorem between the modified $K$-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems for the linear combinations of Jacobi weighted Baskakov–Durrmeyer operators in the Orlicz spaces.

Han , Lingxiong and Bai , Yumei. (2024). Direct, Inverse Theorems of Approximation by Linear Combinations of Weighted Baskakov–Durrmeyer Operators in Orlicz Spaces. Analysis in Theory and Applications. 40 (3). 221-239. doi:10.4208/ata.OA-2022-0013
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