Higher order limit q-Bernstein operators

In this paper we give the estimates of the central moments for the limit q‐Bernstein operators. We introduce the higher order generalization of the limit q‐Bernstein operators and using the moment estimations study the approximation properties of these newly defined operators. It is shown that the h...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2011-09, Vol.34 (13), p.1618-1626
Main Author: Mahmudov, N. I.
Format: Article
Language:English
Subjects:
Approximation
central moment
Estimates
Exact sciences and technology
higher order limit q-Bernstein operator
limit q-Bernstein operator
Mathematical analysis
Mathematics
Operator theory
Operators
positive linear operator
q-Bernstein polynomials
q-derivative
Sciences and techniques of general use
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Summary:In this paper we give the estimates of the central moments for the limit q‐Bernstein operators. We introduce the higher order generalization of the limit q‐Bernstein operators and using the moment estimations study the approximation properties of these newly defined operators. It is shown that the higher order limit q‐Bernstein operators faster than the q‐Bernstein operators for the smooth functions defined on [0, 1]. Copyright © 2011 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
1099-1476
DOI:10.1002/mma.1469