Iterates of a class of discrete linear operators via contraction principle

Commentationes Mathematicae Universitatis Carolinae

Volumn 44, Issue 3, 2003, Pages 555-563

  Agratini, Octavian ^a   Rus, Ioan A ^a  

^a BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Contraction principle; Delta operators; Linear positive operators; Operators of binomial type; Weakly Picard operators

Indexed keywords

EID: 34247604529     PISSN: 00102628     EISSN: 12137243     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. 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
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
3. Cheney E.W., Sharma A On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma (2) 5 (1964), 77-84
4. Kelisky R.P., Rivlin T.J Iterates of Bernstein polynomials, Pacific J. Math. 21 (1967), 511-520
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
6. Mastroianni G., Occorsio M.R Una generalizzatione dell'operatore di Stancu, Rend. Accad. Sci. Fis. Mat. Napoli (4) 45 (1978), 495-511
7. Popoviciu T Remarques sur les polynomes binomiaux, Bul. Soc. Sci. Cluj (Roumanie) 6 (1931), 146-148 (also reproduced in Mathematica (Cluj) 6 (1932), 8-10)
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
9. Rus I.A Weakly Picard mappings, Comment. Math. Univ. Carolinae 34 (1993), no. 4, 769-773
10. Rus I.A Picard operators and applications, Seminar on Fixed Point Theory, Babeş-Bolyai Univ., Cluj-Napoca, 1996
11. Rus I.A Generalized Contractions and Applications, University Press, Cluj-Napoca, 2001
12. Sablonniere P Positive Bernstein-Sheffer operators, J. Approx. Theory 83 (1995), 330-341
13. Stancu D.D Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine Math. Pures Appl. 13 (1968), no. 8, 1173-1194
14. Stancu D.D., Occorsio M.R On approximation by binomial operators of Tiberiu Popoviciu type, Rev. Anal. Numér. Théor. Approx. 27 (1998), no. 1, 167-181