Iterates of a class of discrete linear operators via contraction principle
Agratini, Octavian ; Rus, Ioan A.
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003), p. 555-563 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2003-01-01
Classification:  41A36,  47H10
@article{119408,
     author = {Octavian Agratini and Ioan A. Rus},
     title = {Iterates of a class of discrete linear operators via contraction principle},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {44},
     year = {2003},
     pages = {555-563},
     zbl = {1096.41015},
     mrnumber = {2025820},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119408}
}
Agratini, Octavian; Rus, Ioan A. Iterates of a class of discrete linear operators via contraction principle. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 555-563. http://gdmltest.u-ga.fr/item/119408/

Agratini O. Binomial polynomials and their applications in Approximation Theory, Conferenze del Seminario di Matematica dell'Universita di Bari 281, Roma, 2001, pp.1-22. | MR 1850829 | Zbl 1008.05010

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. | MR 1292247 | Zbl 0924.41001

Cheney E.W.; Sharma A. On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma (2) 5 (1964), 77-84. (1964) | MR 0198074 | Zbl 0146.08202

Kelisky R.P.; Rivlin T.J. Iterates of Bernstein polynomials, Pacific J. Math. 21 (1967), 511-520. (1967) | MR 0212457 | Zbl 0177.31302

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

Mastroianni G.; Occorsio M.R. Una generalizzatione dell'operatore di Stancu, Rend. Accad. Sci. Fis. Mat. Napoli (4) 45 (1978), 495-511. (1978) | MR 0549902

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). (1931) | Zbl 0002.39801

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. (1973) | MR 0345826 | Zbl 0267.05004

Rus I.A. Weakly Picard mappings, Comment. Math. Univ. Carolinae 34 (1993), 4 769-773. (1993) | MR 1263804 | Zbl 0787.54045

Rus I.A. Picard operators and applications, Seminar on Fixed Point Theory, Babeş-Bolyai Univ., Cluj-Napoca, 1996. | Zbl 1031.47035

Rus I.A. Generalized Contractions and Applications, University Press, Cluj-Napoca, 2001. | MR 1947742 | Zbl 0968.54029

Sablonniere P. Positive Bernstein-Sheffer operators, J. Approx. Theory 83 (1995), 330-341. (1995) | MR 1361533 | Zbl 0835.41024

Stancu D.D. Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine Math. Pures Appl. 13 (1968), 8 1173-1194. (1968) | MR 0238001 | Zbl 0167.05001

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. (1998) | MR 1818225 | Zbl 1007.41016