ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
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Approximation in variation by the Meyer-König and Zeller operators; pp. 88–97
PDF | doi: 10.3176/proc.2011.2.03

Authors
Andi Kivinukk, Tarmo Metsmägi
Abstract
The convergence in variation and the rate of approximation of the Meyer-König and Zeller operators are discussed. It is proved that for absolutely continuous functions the rate of approximation can be estimated via the total variation.
References

  1. Abel, U. The complete asymptotic expansion for the Meyer-König and Zeller operators. J. Math. Anal. Appl., 1997, 208, 109–119.
doi:10.1006/jmaa.1997.5295

  2. Adell, J. A. and de la Cal, J. Bernstein-type operators diminish the φ-variation. Constr. Approx., 1996, 12, 489–507.
doi:10.1007/s003659900027

  3. Agratini, O. On the variation detracting property of a class of operators. Appl. Math. Lett., 2006, 19, 1261–1264.
doi:10.1016/j.aml.2005.12.007

  4. Bardaro, C., Butzer, P. L., Stens, R. L., and Vinti, G. Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals. Analysis (Munich), 2003, 23(4), 299–340.

  5. Cheney, E. W. and Sharma, A. Bernstein power series. Canad. J. Math., 1964, 16, 241–253.
doi:10.4153/CJM-1964-023-1

  6. Meyer-König, W. and Zeller, K. Bernsteinische Potenzreihen. Studia Math., 1960, 19, 89–94.

  7. Musielak, J. and Orlicz, W. On generalized variation I. Studia Math., 1959, 18, 11–41.

  8. Radu, C. Variation detracting property of the Bézier type operators. Facta Universitatis (Niš), Ser. Math. Inform., 2008, 23, 23–28.

  9. Trigub, R. M. and Belinsky, E. S. Fourier Analysis and Approximation of Functions. Kluwer Academic Publishers, Dordrecht, 2004.

10. Young, L. C. Sur une généralisation de la notion de variation de puissance pième bornée au sens de N. Wiener, et sur la convergence des séries de Fourier. C. R. Acad. Sci. Paris, 1937, 204(7), 470–472.
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