On convergence of Chlodovsky type Durrmeyer polynomials in variation seminorm

Özlem Öksüzer Yilik; Harun Karsli; Fatma Tasdelen

doi:10.33993/jnaat471-1126

Authors

Özlem Öksüzer Yilik Ankara University, Turkey
Harun Karsli Abant Izzet Baysal University, Turkey
Fatma Tasdelen University of Ankara, Turkey

DOI:

https://doi.org/10.33993/jnaat471-1126

Keywords:

convergence in variation seminorm, Chlodovsky polynomials, Durrmeyer polynomials, rate of convergence, absolutely continuous functions

Abstract views: 480

Abstract

This paper deals with the variation detracting property and rate of approximation of the Chlodovsky type Durrmeyer polynomials in the space of functions of bounded variation with respect to the variation seminorm.

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References

I. Chlodovsky, Sur le développement des fonctions définies dans un interval le infinien séries de polynomes de M. S. Bernstein, Compositio Math., 4 (1937), 380–393.

T. Hermann, Approximation of unbounded functions on unbounded interval, Acta.Math. Hungar., 29 (1977), 393–398, https://doi.org/10.1007/bf01895859. DOI: https://doi.org/10.1007/BF01895859

G. Bleimann, P.L. Butzer and L. Hahn, A Bernstein-type operator approximating continuous functions on the semi-axis, Indag. Math., 42 (1980), 255–262, https://doi.org/10.1016/1385-7258(80)90027-x. DOI: https://doi.org/10.1016/1385-7258(80)90027-X

J.L. Durrmeyer, Une formule d’inversion de la transformée de Laplace: Applications à la théorie des moments, Thèse de 3e Cycle, Faculté des Sciences de l’Université de Paris, 1967.

H. Karsli, P. Pych-Taberska, On the rates of convergence of Chlodovsky–Durrmeyer operators and their Bézier variant, Georgian Math. J.,16 (2009) no. 4, 693–704. DOI: https://doi.org/10.1515/GMJ.2009.693

H. Karsli, Order of convergence of Chlodowsky type Durrmeyer operators for functions with derivatives of bounded variation, Indian J. Pure Appl. Math., 38 (2007) no. 5, 353.

G.G. Lorentz, Bernstein polynomials, University of Toronto Press, Toronto (1953).

C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Convergence in variation andrates of approximation for Bernstein-type polynomials and singular convolution integrals, Analysis (Munich), 23 (2003) no. 4, 299–346, https://doi.org/10.1524/anly.2003.23.4.299. DOI: https://doi.org/10.1524/anly.2003.23.4.299

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

A. Kivinukk, T. Metsmagi, Approximation in variation by the Meyer-König and Zeller operators, Proc. Estonian Acad. Sci., 60 (2011) no. 2, 88–97, https://doi.org/10.3176/proc.2011.2.03. DOI: https://doi.org/10.3176/proc.2011.2.03

H. Karsli, On convergence of Chlodovsky and Chlodovsky-Kantorovich polynomials inthe variation seminorm, Mediterr. J. Math., 10 (2013), 41–56, https://doi.org/10.1007/s00009-012-0186-4. DOI: https://doi.org/10.1007/s00009-012-0186-4

Ö. Öksüzer, H. Karsli, F. Tasdelen, On convergence of Bernstein-Stancu polynomials in the variation seminorm, Numer. Funct. Anal. Optim., 37 (2016) no. 4, 1–20, https://doi.org/10.1080/01630563.2015.1137938 DOI: https://doi.org/10.1080/01630563.2015.1137938

H.Gül ?nce ?arslan, G. Ba?canbaz-Tunca, Convergence in variation for Bernstein-type operators, Mediterr. J. Math., 13 (2015) no. 5, pp. 2577–2592, https://doi.org/10.1007/s00009-015-0640-1. DOI: https://doi.org/10.1007/s00009-015-0640-1

U. Abel and O. Agratini, On the variation detracting property of operators of Balázs and Szabados, Acta Math. Hungarica, 150 (2016) no. 2, 383–395, https://doi.org/10.1007/s10474-016-0642-x. DOI: https://doi.org/10.1007/s10474-016-0642-x

H. Karsli, Ö. Öksüzer Y?l?k, F. Tasdelen, Convergence of the Bernstein–Durrmeyer operators in variation seminorm, Results Math., 72 (yr??), 1257–1270, https://doi.org/10.1007/s00025-017-0653-0. DOI: https://doi.org/10.1007/s00025-017-0653-0

P.L. Butzer and H. Karsli, Voronovskaya-type theorems for derivatives of the Bernstein-Chlodovsky polynomials and the Száasz-Mirakyan operator, Comment. Math., 49 (2009) no. 1, 33–57.

R.M. Trigub and E.S. Belinsky, Fourier Analysis and Approximation of Functions. Kluwer Academic Publishers, Dordrecht (2004) DOI: https://doi.org/10.1007/978-1-4020-2876-2