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On \(L_{p}\)-approximation by iterative combination of Bernstein-Durrmeyer polynomials. (English) Zbl 1216.41014

Summary: We improve the degree of approximation by Bernstein-Durrmeyer polynomials taking their iterates and obtain an error estimate in higher-order approximation.

MSC:

41A30 Approximation by other special function classes
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References:

[1] J. L. Durrmeyer, Une formule’d inversion de la transformee de Laplace: Applications a la Theorie des Moments, M.S. thesis, Faculte des science del’Universite de Paris, Paris, France, 1967.
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[8] E. Hewitt and K. Stromberg, Real and Abstract Analysis, McGraw-Hill, New-York, NY, USA, 1969. · Zbl 0225.26001
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