Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Bleimann; Butzer and Hahn operator; Lebesgue-Denjoy point; rate of convergence
Bleimann; Butzer and Hahn operator; Lebesgue-Denjoy point; rate of convergence
Summary:
For some classes of functions $f$ locally integrable in the sense of Lebesgue or Denjoy-Perron on the interval $[0;\infty )$, the Kantorovich type modification of the Bleimann, Butzer and Hahn operators is considered. The rate of pointwise convergence of these operators at the Lebesgue or Lebesgue-Denjoy points of $f$ is estimated.
References:
[1] Abel U.: On the asymptotic approximation with Bivariate operators of Bleimann, Butzer and Hahn. J. Approx. Theory 97 (1999), 181-198. MR 1676351 | Zbl 0928.41012
[2] Abel U.: On the asymptotic approximation with operators of Bleimann, Butzer and Hahn. Indag. Math. (N.S.) 7 (1996), 1-9. DOI 10.1016/0019-3577(96)88653-8 | MR 1621356 | Zbl 0851.47009
[3] Abel U., Ivan M.: Some identities for the operator of Bleimann, Butzer and Hahn involving divided differences. Calcolo 36 3 (1999), 143-160. DOI 10.1007/s100920050028 | MR 1742307 | Zbl 0931.41013
[4] Abel U., Ivan M.: A Kantorovich variant of the Bleimann, Butzer and Hahn operators. Rend. Circ. Mat. Palermo (2) Suppl. (2002), 68 205-218. MR 1975505 | Zbl 1012.41016
[5] Bleimann G., Butzer P.L., Hahn L.: A Bernstein-type operator approximating continuous functions of the semi-axis. Indag. Math. 42 (1980), 255-262. MR 0587054
[6] de la Cal J., Luquin F.: A note on limiting properties of some Bernstein-type operators. J. Approx. Theory 68 (1992), 322-329. DOI 10.1016/0021-9045(92)90108-Z | MR 1152222
[7] Della Vecchia B.: Some properties of a rational operator of Bernstein-type. in Progress in Approximation Theory (P. Nevai and A. Pinkus, Eds.), Academic Press, New York, 1991, pp.177-185. MR 1114772
[8] Hermann T.: On the operator of Bleimann, Butzer and Hahn. Colloq. Math. Soc. János Bolyai 58 (1991), 355-360. MR 1211445 | Zbl 0784.41016
[9] Khan R.A.: A note on a Bernstein-type operator of Bleimann, Butzer and Hahn. J. Approx. Theory 53 (1988), 295-303. DOI 10.1016/0021-9045(88)90024-X | MR 0947433 | Zbl 0676.41024
[10] Khan R.A.: Some properties of a Bernstein-type operator of Bleimann, Butzer and Hahn. in Progress in Approximation Theory (P. Nevai and A. Pinkus, Eds.), Academic Press, New York, 1991, pp.497-504. MR 1114792
[11] Jayasri C., Sitaraman Y.: On a Bernstein type operator of Bleimann, Butzer and Hahn. J. Comput. Appl. Math. 47 2 (1993), 267-272. DOI 10.1016/0377-0427(93)90008-Y | MR 1237316 | Zbl 0779.41008
[12] Nowak G., Pych-Taberska P.: Approximation properties of the generalized Favard-Kantorovich operators. Comment. Math. Prace Mat. 39 (1999), 139-152. MR 1739024 | Zbl 0970.41014
[13] Saks S.: Theory of the Integral. New York, 1937. Zbl 0017.30004
[14] Totik V.: Uniform approximation by Bernstein-type operators. Indag. Math. 46 (1984), 87-93. MR 0748982 | Zbl 0538.41035
Search
Partner of
