Higher Order Approximation of Continuous Functions by a Modified Meyer-König and Zeller-Type Operator
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915348387725312 |
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| author | Gadjev, Ivan Parvanov, Parvan Uluchev, Rumen |
| author_facet | Gadjev, Ivan Parvanov, Parvan Uluchev, Rumen |
| contents | A new Goodman-Sharma type modification of the Meyer-König and Zeller operator for approximation of bounded continuous functions on [0,1) is presented. We estimate the approximation error of the proposed operator and prove direct and strong converse theorems with respect to a related K-functional. The operator is linear but not a positive one. However it benefits a better order of approximation compared to the Goodman-Sharma variant of Meyer-König and Zeller type operator investigated by Ivanov and Parvanov in 2012. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Order Approximation of Continuous Functions by a Modified Meyer-König and Zeller-Type Operator Gadjev, Ivan Parvanov, Parvan Uluchev, Rumen Classical Analysis and ODEs 41A35, 41A10, 41A25, 41A27, 41A17 A new Goodman-Sharma type modification of the Meyer-König and Zeller operator for approximation of bounded continuous functions on [0,1) is presented. We estimate the approximation error of the proposed operator and prove direct and strong converse theorems with respect to a related K-functional. The operator is linear but not a positive one. However it benefits a better order of approximation compared to the Goodman-Sharma variant of Meyer-König and Zeller type operator investigated by Ivanov and Parvanov in 2012. |
| title | Higher Order Approximation of Continuous Functions by a Modified Meyer-König and Zeller-Type Operator |
| topic | Classical Analysis and ODEs 41A35, 41A10, 41A25, 41A27, 41A17 |
| url | https://arxiv.org/abs/2506.14392 |