Approximation by q‐Bernstein Polynomials in the Case q → 1+

Xuezhi Wu

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let Bn,q(f; x), q ∈ (0, ∞) be the q‐Bernstein polynomials of a function f ∈ C[0,1]. It has been known that, in general, the sequence Bn,qn(f) with qn → 1+ is not an approximating sequence for f ∈ C[0,1], in contrast to the standard case qn → 1−. In this paper, we give the sufficient and necessary condition under which the sequence Bn,qn(f) approximates f for any f ∈ C[0,1] in the case qn > 1. Based on this condition, we get that if 1 1, then the sequence (qn) satisfies lim¯n→∞n(qn-12)≤ln.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:259491

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