Approximation by -Bernstein Polynomials in the Case

Xuezhi Wu

Abstract and Applied Analysis, 2014, vol. 2014, 1-6

Abstract:

Let , be the -Bernstein polynomials of a function . It has been known that, in general, the sequence with is not an approximating sequence for , in contrast to the standard case . In this paper, we give the sufficient and necessary condition under which the sequence approximates for any in the case . Based on this condition, we get that if for sufficiently large , then approximates for any . On the other hand, if can approximate for any in the case , then the sequence satisfies .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:259491

DOI: 10.1155/2014/259491

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