On the Rates of Approximation of Bernstein Type Operators

Xiao Ming Zeng; Fuhua Cheng

doi:10.1006/jath.2000.3538

On the Rates of Approximation of Bernstein Type Operators

Xiao Ming Zeng, Fuhua Cheng

Computer Science

Research output: Contribution to journal › Article › peer-review

44 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 language	English
Pages (from-to)	242-256
Number of pages	15
Journal	Journal of Approximation Theory
Volume	109
Issue number	2
DOIs	https://doi.org/10.1006/jath.2000.3538
State	Published - Apr 2001

Bibliographical note

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

Funding

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

Funders	Funder number
Fujian Provincial Science Foundation of China
National Natural Science Foundation of China (NSFC)	19871068

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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10.1006/jath.2000.3538

Cite this

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title = "On the Rates of Approximation of Bernstein Type Operators",

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 Sz{\'a}sz 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.",

author = "Zeng, \{Xiao Ming\} and Fuhua Cheng",

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

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language = "English",

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AU - Cheng, Fuhua

N1 - Funding Information: 1Supported by NSFC 19871068 and Fujian Provincial Science Foundation of China.

PY - 2001/4

Y1 - 2001/4

N2 - 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.

AB - 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.

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DO - 10.1006/jath.2000.3538

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IS - 2

ER -

On the Rates of Approximation of Bernstein Type Operators

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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