| Title:
|
Iterates of a class of discrete linear operators via contraction principle (English) |
| Author:
|
Agratini, Octavian |
| Author:
|
Rus, Ioan A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
555-563 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed. (English) |
| Keyword:
|
linear positive operators |
| Keyword:
|
contraction principle |
| Keyword:
|
weakly Picard operators |
| Keyword:
|
delta operators |
| Keyword:
|
operators of binomial type |
| MSC:
|
41A36 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1096.41015 |
| idMR:
|
MR2025820 |
| . |
| Date available:
|
2009-01-08T19:31:03Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119408 |
| . |
| Reference:
|
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| Reference:
|
[2] Altomare F., Campiti M.: Korovkin-Type Approximation Theory and its Applications.de Gruyter Series Studies in Mathematics, Vol.17, Walter de Gruyter, Berlin-New York, 1994. Zbl 0924.41001, MR 1292247 |
| Reference:
|
[3] Cheney E.W., Sharma A.: On a generalization of Bernstein polynomials.Riv. Mat. Univ. Parma (2) 5 (1964), 77-84. Zbl 0146.08202, MR 0198074 |
| Reference:
|
[4] Kelisky R.P., Rivlin T.J.: Iterates of Bernstein polynomials.Pacific J. Math. 21 (1967), 511-520. Zbl 0177.31302, MR 0212457 |
| Reference:
|
[5] Lupaş A.: Approximation operators of binomial type.New developments in approximation theory (Dortmund, 1998), pp.175-198, International Series of Numerical Mathematics, Vol.132, Birkhäuser Verlag Basel/Switzerland, 1999. MR 1724919 |
| Reference:
|
[6] Mastroianni G., Occorsio M.R.: Una generalizzatione dell'operatore di Stancu.Rend. Accad. Sci. Fis. Mat. Napoli (4) 45 (1978), 495-511. MR 0549902 |
| Reference:
|
[7] Popoviciu T.: Remarques sur les polynômes binomiaux.Bul. Soc. Sci. Cluj (Roumanie) 6 (1931), 146-148 (also reproduced in Mathematica (Cluj) 6 (1932), 8-10). Zbl 0002.39801 |
| Reference:
|
[8] Rota G.-C., Kahaner D., Odlyzko A.: On the Foundations of Combinatorial Theory. VIII. Finite operator calculus.J. Math. Anal. Appl. 42 (1973), 685-760. Zbl 0267.05004, MR 0345826 |
| Reference:
|
[9] Rus I.A.: Weakly Picard mappings.Comment. Math. Univ. Carolinae 34 (1993), 4 769-773. Zbl 0787.54045, MR 1263804 |
| Reference:
|
[10] Rus I.A.: Picard operators and applications.Seminar on Fixed Point Theory, Babeş-Bolyai Univ., Cluj-Napoca, 1996. Zbl 1031.47035 |
| Reference:
|
[11] Rus I.A.: Generalized Contractions and Applications.University Press, Cluj-Napoca, 2001. Zbl 0968.54029, MR 1947742 |
| Reference:
|
[12] Sablonniere P.: Positive Bernstein-Sheffer operators.J. Approx. Theory 83 (1995), 330-341. Zbl 0835.41024, MR 1361533 |
| Reference:
|
[13] Stancu D.D.: Approximation of functions by a new class of linear polynomial operators.Rev. Roumaine Math. Pures Appl. 13 (1968), 8 1173-1194. Zbl 0167.05001, MR 0238001 |
| Reference:
|
[14] Stancu D.D., Occorsio M.R.: On approximation by binomial operators of Tiberiu Popoviciu type.Rev. Anal. Numér. Théor. Approx. 27 (1998), 1 167-181. Zbl 1007.41016, MR 1818225 |
| . |
