| Title:
|
Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators (English) |
| Author:
|
Nowak, Grzegorz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
67-78 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Bleimann |
| Keyword:
|
Butzer and Hahn operator |
| Keyword:
|
Lebesgue-Denjoy point |
| Keyword:
|
rate of convergence |
| MSC:
|
41A25 |
| idZBL:
|
Zbl 1212.41051 |
| idMR:
|
MR2433625 |
| . |
| Date available:
|
2009-05-05T17:06:33Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119702 |
| . |
| Reference:
|
[1] Abel U.: On the asymptotic approximation with Bivariate operators of Bleimann, Butzer and Hahn.J. Approx. Theory 97 (1999), 181-198. Zbl 0928.41012, MR 1676351 |
| Reference:
|
[2] Abel U.: On the asymptotic approximation with operators of Bleimann, Butzer and Hahn.Indag. Math. (N.S.) 7 (1996), 1-9. Zbl 0851.47009, MR 1621356, 10.1016/0019-3577(96)88653-8 |
| Reference:
|
[3] Abel U., Ivan M.: Some identities for the operator of Bleimann, Butzer and Hahn involving divided differences.Calcolo 36 3 (1999), 143-160. Zbl 0931.41013, MR 1742307, 10.1007/s100920050028 |
| Reference:
|
[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. Zbl 1012.41016, MR 1975505 |
| Reference:
|
[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 |
| Reference:
|
[6] de la Cal J., Luquin F.: A note on limiting properties of some Bernstein-type operators.J. Approx. Theory 68 (1992), 322-329. MR 1152222, 10.1016/0021-9045(92)90108-Z |
| Reference:
|
[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 |
| Reference:
|
[8] Hermann T.: On the operator of Bleimann, Butzer and Hahn.Colloq. Math. Soc. János Bolyai 58 (1991), 355-360. Zbl 0784.41016, MR 1211445 |
| Reference:
|
[9] Khan R.A.: A note on a Bernstein-type operator of Bleimann, Butzer and Hahn.J. Approx. Theory 53 (1988), 295-303. Zbl 0676.41024, MR 0947433, 10.1016/0021-9045(88)90024-X |
| Reference:
|
[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 |
| Reference:
|
[11] Jayasri C., Sitaraman Y.: On a Bernstein type operator of Bleimann, Butzer and Hahn.J. Comput. Appl. Math. 47 2 (1993), 267-272. Zbl 0779.41008, MR 1237316, 10.1016/0377-0427(93)90008-Y |
| Reference:
|
[12] Nowak G., Pych-Taberska P.: Approximation properties of the generalized Favard-Kantorovich operators.Comment. Math. Prace Mat. 39 (1999), 139-152. Zbl 0970.41014, MR 1739024 |
| Reference:
|
[13] Saks S.: Theory of the Integral.New York, 1937. Zbl 0017.30004 |
| Reference:
|
[14] Totik V.: Uniform approximation by Bernstein-type operators.Indag. Math. 46 (1984), 87-93. Zbl 0538.41035, MR 0748982 |
| . |
