Approximation by the modified λ-Bernstein-polynomial in terms of basis function
In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin's theorem, establish a local appro...
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| Format: | Article |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024217?viewType=HTML |
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| author | Mohammad Ayman-Mursaleen Md. Nasiruzzaman Nadeem Rao Mohammad Dilshad Kottakkaran Sooppy Nisar |
| author_facet | Mohammad Ayman-Mursaleen Md. Nasiruzzaman Nadeem Rao Mohammad Dilshad Kottakkaran Sooppy Nisar |
| author_sort | Mohammad Ayman-Mursaleen |
| collection | DOAJ |
| description | In this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin's theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre's $ K $-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja. |
| first_indexed | 2024-03-08T05:34:11Z |
| format | Article |
| id | doaj.art-a59eaed3a9ec41bba1f2a0445cfb17e8 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:34:11Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a59eaed3a9ec41bba1f2a0445cfb17e82024-02-06T01:21:50ZengAIMS PressAIMS Mathematics2473-69882024-01-01924409442610.3934/math.2024217Approximation by the modified λ-Bernstein-polynomial in terms of basis functionMohammad Ayman-Mursaleen0Md. Nasiruzzaman 1Nadeem Rao2Mohammad Dilshad 3Kottakkaran Sooppy Nisar 41. School of Information and Physical Sciences, The University of Newcastle, University Drive, Callaghan, New South Wales 2308, Australia2. Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 4279, Tabuk 71491, Saudi Arabia3. Department of Mathematics, University Centre for Research and Development, Chandigarh University, Mohali-140413, Punjab, India2. Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 4279, Tabuk 71491, Saudi Arabia4. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaIn this article by means of shifted knots properties, we introduce a new type of coupled Bernstein operators for Bézier basis functions. First, we construct the operators based on shifted knots properties of Bézier basis functions then investigate the Korovkin's theorem, establish a local approximation theorem, and provide a convergence theorem for Lipschitz continuous functions and Peetre's $ K $-functional. In addition, we also obtain an asymptotic formula of the type Voronovskaja.https://www.aimspress.com/article/doi/10.3934/math.2024217?viewType=HTMLbernstein-polynomial$ \lambda $-bernstein-polynomialbézier basis functionshifted knotsmodulus of continuitylipschitz maximal functionspeetre's $ k $-functional |
| spellingShingle | Mohammad Ayman-Mursaleen Md. Nasiruzzaman Nadeem Rao Mohammad Dilshad Kottakkaran Sooppy Nisar Approximation by the modified λ-Bernstein-polynomial in terms of basis function AIMS Mathematics bernstein-polynomial $ \lambda $-bernstein-polynomial bézier basis function shifted knots modulus of continuity lipschitz maximal functions peetre's $ k $-functional |
| title | Approximation by the modified λ-Bernstein-polynomial in terms of basis function |
| title_full | Approximation by the modified λ-Bernstein-polynomial in terms of basis function |
| title_fullStr | Approximation by the modified λ-Bernstein-polynomial in terms of basis function |
| title_full_unstemmed | Approximation by the modified λ-Bernstein-polynomial in terms of basis function |
| title_short | Approximation by the modified λ-Bernstein-polynomial in terms of basis function |
| title_sort | approximation by the modified λ bernstein polynomial in terms of basis function |
| topic | bernstein-polynomial $ \lambda $-bernstein-polynomial bézier basis function shifted knots modulus of continuity lipschitz maximal functions peetre's $ k $-functional |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024217?viewType=HTML |
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