On the composite Bernstein type quadrature formula

Dan Bărbosu; Dan Miclăuş

doi:10.33993/jnaat391-915

Authors

Dan Bărbosu North University of Baia Mare, Romania
Dan Miclăuş North University of Baia Mare, Romania

DOI:

https://doi.org/10.33993/jnaat391-915

Keywords:

Bernstein operator, Bernstein approximation formula, Bernstein quadrature formula, divided differences, remainder term

Abstract views: 316

Abstract

Considering a given function \(f\in C[0,1]\), the interval \([0,1]\) is divided in \(m\) equally spaced subintervals \(\left[\tfrac{k-1}{m},\tfrac{k}{m}\right]\), \(k=\overline{1,m}\). On each of such type of interval the Bernstein approximation formula is applied and a corresponding Bernstein type quadrature formula is obtained. Making the sum of mentioned quadrature formulas, the composite Bernstein type quadrature formula is obtained.

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References

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