On the Rate of Convergence of Two Bernstein–Bézier Type Operators for Bounded Variation Functions

✍ Scribed by Xiaoming Zeng; Alain Piriou

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 285 KB
• Volume: 95
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1997.3227

✦ Synopsis

In this paper we study the rate of convergence of two Bernstein Be zier type operators B (:) n and L (:) n for bounded variation functions. By means of construction of suitable functions and the method of Bojanic and Vuillemier (J. Approx. Theory 31 (1981), 67 79), using some results of probability theory, we obtain asymptotically optimal estimations of B (:) n and L (:) n for bounded variation functions at points of continuity and points of discontinuity.