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2009 | 29 | 1 | 53-66
Tytuł artykułu

Rates of convergence of Chlodovsky-Kantorovich polynomials in classes of locally integrable functions

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Abstrakty
EN
In this paper we establish an estimation for the rate of pointwise convergence of the Chlodovsky-Kantorovich polynomials for functions f locally integrable on the interval [0,∞). In particular, corresponding estimation for functions f measurable and locally bounded on [0,∞) is presented, too.
Twórcy
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
Bibliografia
  • [1] J. Albrycht and J. Radecki, On a generalization of the theorem of Voronovskaya, Zeszyty Naukowe UAM, Zeszyt 2, Poznań (1960), 1-7.
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  • [3] P.L. Butzer and H. Karsli, Voronovskaya-type theorems for derivatives of the Bernstein-Chlodovsky polynomials and the Szász-Mirakyan operator, Comment. Math., to appear.
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  • [5] I. Chlodovsky, Sur le développement des fonctions définies dans un intervalle infini en séries de polynomes de M.S. Bernstein, Compositio Math. 4 (1937), 380-393.
  • [6] M. Heilmann, Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory Appl. 5 (1) (1989), 105-127.
  • [7] H. Karsli and E. Ibikli, Rate of convergence of Chlodovsky type Bernstein operators for functions of bounded variation, Numer. Funct. Anal. Optim. 28 (3-4) (2007), 367-378.
  • [8] G.G. Lorentz, Bernstein Polynomials, University of Toronto Press, Toronto, 1953.
  • [9] P. Pych-Taberska, Some properties of the Bézier-Kantorovich type operators, J. Approx. Theory 123 (2003), 256-269.
  • [10] L.C. Young, General inequalities for Stieltjes integrals and the convergence of Fourier series, Math. Annalen 115 (1938), 581-612.
  • [11] X.M. Zeng, Bounds for Bernstein basis functions and Meyer-König and Zeller basis functions, J. Math. Anal. Appl. 219 (2) (1998), 364-376.
  • [12] X.M. Zeng and A. Piriou On the rate of convergence of two Berstein-Bézier type operators for bounded variation functions, J. Approx. Theory 95 (1998), 369-387.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1104
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