| Title:
|
Remarks on an article of J.P. King (English) |
| Author:
|
Gonska, Heiner |
| Author:
|
Piţul, Paula |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
645-652 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present note discusses an interesting positive linear operator which was recently introduced by J.P. King. New estimates in terms of the first and second modulus of continuity are given, and iterates of the operators are considered as well. For general King operators the second moments are minimized. (English) |
| Keyword:
|
positive linear operators |
| Keyword:
|
degree of approximation |
| Keyword:
|
contraction principle |
| Keyword:
|
second order modulus |
| Keyword:
|
second moments |
| MSC:
|
41A25 |
| MSC:
|
41A36 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1121.41013 |
| idMR:
|
MR2259496 |
| . |
| Date available:
|
2009-05-05T16:54:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119556 |
| . |
| Reference:
|
[1] Agratini O., Rus I.A.: Iterates of a class of discrete linear operators.Comment. Math. Univ. Carolinae 44 (2003), 555-563. Zbl 1096.41015, MR 2025820 |
| Reference:
|
[2] Beresin I.S., Zhidkov N.P.: Numerische Methoden II.VEB Deutscher Verlag der Wissenschaften, Berlin, 1971. |
| Reference:
|
[3] Kelisky R.P., Rivlin T.J.: Iterates of Bernstein polynomials.Pacific J. Math. 21 (1967), 511-520. Zbl 0177.31302, MR 0212457 |
| Reference:
|
[4] King P.J.: Positive linear operators which preserve $x^2$.Acta Math. Hungar. 99 (2003), 203-208. MR 1973095 |
| Reference:
|
[5] Mamedov R.G.: On the order of approximation of functions by sequences of linear positive operators (Russian).Dokl. Akad. Nauk SSSR 128 (1959), 674-676. MR 0110017 |
| Reference:
|
[6] Păltănea R.: Approximation by linear positive operators: Estimates with second order moduli.Ed. Univ. Transilvania, Braşov, 2003. |
| Reference:
|
[7] Rus I.A.: Iterates of Bernstein operators, via contraction principle.J. Math. Anal. Appl. 292 (2004), 259-261. Zbl 1056.41004, MR 2050229 |
| Reference:
|
[8] Shisha O., Mond B.: The degree of convergence of linear positive operators.Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 1196-1200. MR 0230016 |
| . |
