A note on Lototsky–Bernstein bases
Abstract In this note, we study some approximation properties on a class of special Lototsky–Bernstein bases. We focus on approximation of | x | $|x|$ on [ − 1 , 1 ] $[-1,1]$ by an approximation process generated from fixed points on Lototsky–Bernstein bases. Our first result shows that the approxim...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-02-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-024-03076-7 |
| Summary: | Abstract In this note, we study some approximation properties on a class of special Lototsky–Bernstein bases. We focus on approximation of | x | $|x|$ on [ − 1 , 1 ] $[-1,1]$ by an approximation process generated from fixed points on Lototsky–Bernstein bases. Our first result shows that the approximation procedure p n ( x ) $p_{n}(x)$ to | x | $|x|$ preserves good shapes on [ − 1 , 1 ] $[-1,1]$ . Moreover, some convergence results and inequalities are derived. Our second main result states that the rate convergence of the approximation is O ( n − 2 ) $O(n^{-2})$ . |
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| ISSN: | 1029-242X |