On the Rates of Approximation of Bernstein Type Operators

Xiao Ming Zeng, Fuhua Cheng

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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 languageEnglish
Pages (from-to)242-256
Number of pages15
JournalJournal of Approximation Theory
Volume109
Issue number2
DOIs
StatePublished - Apr 2001

Bibliographical note

Funding Information:
1Supported by NSFC 19871068 and Fujian Provincial Science Foundation of China.

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics (all)
  • Applied Mathematics

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