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2013 A Survey of Results on the Limit q-Bernstein Operator
Sofiya Ostrovska
J. Appl. Math. 2013: 1-7 (2013). DOI: 10.1155/2013/159720


The limit q-Bernstein operator Bq emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplary model for the study of the convergence of the q-operators. Over the past years, the limit q-Bernstein operator has been studied widely from different perspectives. It has been shown that Bq is a positive shape-preserving linear operator on C[0,1] with Bq=1. Its approximation properties, probabilistic interpretation, the behavior of iterates, and the impact on the smoothness of a function have already been examined. In this paper, we present a review of the results on the limit q-Bernstein operator related to the approximation theory. A complete bibliography is supplied.


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Sofiya Ostrovska. "A Survey of Results on the Limit q-Bernstein Operator." J. Appl. Math. 2013 1 - 7, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1268.81094
MathSciNet: MR3039718
Digital Object Identifier: 10.1155/2013/159720

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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