Local smoothness of functions and Bernstein-Durrmeyer operators

H. H. Gonska; D. X. Zhou

doi:10.1016/0898-1221(95)00088-7

Local smoothness of functions and Bernstein-Durrmeyer operators

H. H. Gonska
, D. X. Zhou

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

Abstract

Continuous functions satisfying a local Lipschitz condition of order α(0 <α <1) on any subset of [0, 1] are characterized by the local rate of convergence of Bernstein-Durrmeyer operators. As an application, we give an algorithm for singular detection. A new direct estimate for the approximation of continuous functions by Bernstein-Durrmeyer operators and Kantorovich operators is also presented. © 1995.

Original language	English
Pages (from-to)	83-101
Journal	Computers and Mathematics with Applications
Volume	30
Issue number	3-6
DOIs	https://doi.org/10.1016/0898-1221(95)00088-7
Publication status	Published - Sept 1995
Externally published	Yes

Research Keywords

Bernstein type operators
Bernstein-Durrmeyer operators
Kantorovich operators
Local Lipschitz conditions
Singular detection

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title = "Local smoothness of functions and Bernstein-Durrmeyer operators",

abstract = "Continuous functions satisfying a local Lipschitz condition of order α(0 <α <1) on any subset of [0, 1] are characterized by the local rate of convergence of Bernstein-Durrmeyer operators. As an application, we give an algorithm for singular detection. A new direct estimate for the approximation of continuous functions by Bernstein-Durrmeyer operators and Kantorovich operators is also presented. {\textcopyright} 1995.",

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author = "Gonska, \{H. H.\} and Zhou, \{D. X.\}",

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doi = "10.1016/0898-1221(95)00088-7",

language = "English",

volume = "30",

pages = "83--101",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

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TY - JOUR

T1 - Local smoothness of functions and Bernstein-Durrmeyer operators

AU - Gonska, H. H.

AU - Zhou, D. X.

PY - 1995/9

Y1 - 1995/9

N2 - Continuous functions satisfying a local Lipschitz condition of order α(0 <α <1) on any subset of [0, 1] are characterized by the local rate of convergence of Bernstein-Durrmeyer operators. As an application, we give an algorithm for singular detection. A new direct estimate for the approximation of continuous functions by Bernstein-Durrmeyer operators and Kantorovich operators is also presented. © 1995.

AB - Continuous functions satisfying a local Lipschitz condition of order α(0 <α <1) on any subset of [0, 1] are characterized by the local rate of convergence of Bernstein-Durrmeyer operators. As an application, we give an algorithm for singular detection. A new direct estimate for the approximation of continuous functions by Bernstein-Durrmeyer operators and Kantorovich operators is also presented. © 1995.

KW - Bernstein type operators

KW - Bernstein-Durrmeyer operators

KW - Kantorovich operators

KW - Local Lipschitz conditions

KW - Singular detection

UR - https://www.scopus.com/pages/publications/58149323078

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-58149323078&origin=recordpage

U2 - 10.1016/0898-1221(95)00088-7

DO - 10.1016/0898-1221(95)00088-7

M3 - RGC 21 - Publication in refereed journal

SN - 0898-1221

VL - 30

SP - 83

EP - 101

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 3-6

ER -

Local smoothness of functions and Bernstein-Durrmeyer operators

Abstract

Research Keywords

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