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2012 On the Sets of Convergence for Sequences of the q -Bernstein Polynomials with q > 1
Sofiya Ostrovska, Ahmet Yaşar Özban
Abstr. Appl. Anal. 2012: 1-19 (2012). DOI: 10.1155/2012/185948

Abstract

The aim of this paper is to present new results related to the convergence of the sequence of the q -Bernstein polynomials { B n , q ( f ; x ) } in the case q > 1 , where f is a continuous function on [ 0,1 ] . It is shown that the polynomials converge to f uniformly on the time scale 𝕁 q = { q - j } j = 0 { 0 } , and that this result is sharp in the sense that the sequence { B n , q ( f ; x ) } n = 1 may be divergent for all x R 𝕁 q . Further, the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper, the results are illustrated by numerical examples.

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Sofiya Ostrovska. Ahmet Yaşar Özban. "On the Sets of Convergence for Sequences of the q -Bernstein Polynomials with q > 1 ." Abstr. Appl. Anal. 2012 1 - 19, 2012. https://doi.org/10.1155/2012/185948

Information

Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1254.41013
MathSciNet: MR2970007
Digital Object Identifier: 10.1155/2012/185948

Rights: Copyright © 2012 Hindawi

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