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.
|Number of pages||15|
|Journal||Journal of Approximation Theory|
|State||Published - Apr 2001|
Bibliographical noteFunding Information:
1Supported by NSFC 19871068 and Fujian Provincial Science Foundation of China.
ASJC Scopus subject areas
- Numerical Analysis
- Mathematics (all)
- Applied Mathematics