Iterated boolean sums of Bernstein and related operators

Ioan Raşa

doi:10.33993/jnaat351-1018

Authors

Ioan Raşa Technical University of Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat351-1018

Keywords:

Bernstein operators and the associated semigroup, Boolean sums

Abstract views: 252

Abstract

Let \((T(t))_{t\geq0}\) be the semigroup associated with the classical Bernstein operators \((B_{n})_{n\geq1}\) on \(C[0,1]\). We obtain rates of convergence for iterated boolean sums of the operators \(T\left( \frac{1}{n}\right) .\)

Downloads

Download data is not yet available.

References

Agrawal, P.N. and Kasana, H.S., On the iterative combinations of Bernstein polynomials, Demonstratio Math., 17, pp. 777-783, 1984. DOI: https://doi.org/10.1515/dema-1984-0320

Altomare, F. and Campiti, M., Korovkin-type Approximation Theory and its Applications, Walter de Gruyter, Berlin - New York, 1994. DOI: https://doi.org/10.1515/9783110884586

Felbecker, G., Linearkombinationen von iterierten Bernsteinoperatoren, Manuscripta Math., 29, pp. 229-248, 1979. DOI: https://doi.org/10.1007/BF01303629

Gonska, H.H. and Zhou, X.L., Approximation theorems for the iterated Boolean sums of Bernstein operators, J. Comp. Appl. Math., 53, pp. 21-31, 1994. DOI: https://doi.org/10.1016/0377-0427(92)00133-T

Mastroianni, G. and Occorsio, M.R., Una generalizzazione dell'operatore di Bernstein, Rend. Accad. Sci. Mat. Fis. Nat. Napoli, 44, pp. 151-169, 1977.

Micchelli, C.A., The saturation class and iterates of the Bernstein polynomials, J. Approximation Theory, 8, pp. 1-18, 1973. DOI: https://doi.org/10.1016/0021-9045(73)90028-2

Rasa, I., Sur les fonctionnelles de la forme simple au sens de T. Popoviciu, Rev. Anal. Numér. Théor. Approx., 9, pp. 261-268, 1980, http://ictp.acad.ro/jnaat/journal/article/view/1980-vol9-no2-art12

Rasa, I., Estimates for the semigroup associated with Bernstein operators, Rev. Anal. Numér. Théor. Approx., 33, 243-245, 2004, http://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no2-art17

Vladislav, T. and Rasa, I., Analiză Numerică. Aproximare, problema lui Cauchy abstractă, proiectori Altomare, Editura Tehnică, Bucureşti, 1999.