Abstract
Asymptotic behavior of two Bernstein-type operators is studied in this paper. In the first case, the rate of convergence of a Bernstein operator for a bounded function f is studied at points x where f(x+) and f(x-) exist. In the second case, the rate of convergence of a Szász operator for a function f whose derivative is of bounded variation is studied at points x where f(x+) and f(x-) exist. Estimates of the rate of convergence are obtained for both cases and the estimates are the best possible for continuous points.
Original language | English |
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Pages (from-to) | 242-256 |
Number of pages | 15 |
Journal | Journal of Approximation Theory |
Volume | 109 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2001 |
Bibliographical note
Funding Information:1Supported by NSFC 19871068 and Fujian Provincial Science Foundation of China.
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- General Mathematics
- Applied Mathematics