On the rate of convergence of two Bernstein-Bezier type operators for bounded variation functions

Authors
Zeng, XM Piriou, A
Citation
Xm. Zeng et A. Piriou, On the rate of convergence of two Bernstein-Bezier type operators for bounded variation functions, J APPROX TH, 95(3), 1998, pp. 369-387
Citations number
14
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF APPROXIMATION THEORY
ISSN journal
00219045 → ACNP
Volume
95
Issue
3
Year of publication
1998
Pages
369 - 387
Database
ISI
SICI code
0021-9045(199812)95:3<369:OTROCO>2.0.ZU;2-X
Abstract
In this paper we study the rate of convergence of two Bernstein-Bezier type operators B-n((alpha)) and L-n((alpha)) for bounded variation functions. B y means of construction of suitable Functions and the method of Bojanic and Vuillemier (J. Approx. Theory 31 (1981), 67-79), using some results of pro bability theory, we obtain asymptotically optimal estimations of B-n((alpha )) and L-n((alpha)) for bounded variation functions at points of continuity and points of discontinuity. (C) 1998 Academic Press.