On a New Modification of Baskakov Operators with Higher Order of Approximation
A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo>&...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/1/64 |
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| Summary: | A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mspace width="0.166667em"></mspace><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>. We study the approximation error of the proposed operator. Our main results are a direct theorem and strong converse theorem with respect to a related K-functional. Both theorems give complete characterization of the uniform approximation error in means of the K-functional. The new operator suggested by the authors is linear but non-positive. However, it has the advantage of a higher order of approximation compared to the Goodman–Sharma variant of the Baskakov operator defined in 2005 by Finta. The results of computational simulations are given. |
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| ISSN: | 2227-7390 |