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@article{DMDICO_2009_29_1_a3, author = {Pych-Taberska, Paulina}, title = {Rates of convergence of {Chlodovsky-Kantorovich} polynomials in classes of locally integrable functions}, journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization}, pages = {53--66}, publisher = {mathdoc}, volume = {29}, number = {1}, year = {2009}, zbl = {1195.41017}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a3/} }
TY - JOUR AU - Pych-Taberska, Paulina TI - Rates of convergence of Chlodovsky-Kantorovich polynomials in classes of locally integrable functions JO - Discussiones Mathematicae. Differential Inclusions, Control and Optimization PY - 2009 SP - 53 EP - 66 VL - 29 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a3/ LA - en ID - DMDICO_2009_29_1_a3 ER -
%0 Journal Article %A Pych-Taberska, Paulina %T Rates of convergence of Chlodovsky-Kantorovich polynomials in classes of locally integrable functions %J Discussiones Mathematicae. Differential Inclusions, Control and Optimization %D 2009 %P 53-66 %V 29 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a3/ %G en %F DMDICO_2009_29_1_a3
Pych-Taberska, Paulina. Rates of convergence of Chlodovsky-Kantorovich polynomials in classes of locally integrable functions. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 29 (2009) no. 1, pp. 53-66. http://geodesic.mathdoc.fr/item/DMDICO_2009_29_1_a3/
[1] J. Albrycht and J. Radecki, On a generalization of the theorem of Voronovskaya, Zeszyty Naukowe UAM, Zeszyt 2, Poznań (1960), 1-7.
[2] R. Bojanic and O. Shisha, Degree of L₁ approximation to integrable functions by modified Bernstein polynomials, J. Approx. Theory 13 (1975), 66-72.
[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.
[4] Z.A. Chanturiya, Modulus of variation of functions and its application in the theory of Fourier series, Dokl. Akad. Nauk SSSR 214 (1974), 63-66.
[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.