On the rates of approximation of Bernstein type operators

Citation
Xm. Zeng et Ff. Cheng, On the rates of approximation of Bernstein type operators, J APPROX TH, 109(2), 2001, pp. 242-256
Citations number
9
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPROXIMATION THEORY
ISSN journal
00219045 → ACNP
Volume
109
Issue
2
Year of publication
2001
Pages
242 - 256
Database
ISI
SICI code
0021-9045(200104)109:2<242:OTROAO>2.0.ZU;2-Y
Abstract
Asymptotic behavior of two Bernstein-type operators is studied in this pape r. In the first case, the rate of convergence of a Bcrnstein 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 Szasz operator for a funct ion 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 F or both cases and the estimates are the best possible for continuous points . (C) 2001 Academic Press.