On the Sets of Convergence for Sequences of the q‐Bernstein Polynomials with q > 1

Sofiya Ostrovska and Ahmet Yaşar Özban

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: The aim of this paper is to present new results related to the convergence of the sequence of the q‐Bernstein polynomials {Bn,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 𝕁q={q-j} j=0∞∪{0}, and that this result is sharp in the sense that the sequence {Bn,q(f;x)} n=1∞ may be divergent for all x ∈ R∖𝕁q. Further, the impossibility of the uniform approximation for the Weierstrass‐type functions is established. Throughout the paper, the results are illustrated by numerical examples.

Date: 2012
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https://doi.org/10.1155/2012/185948

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:185948

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