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.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


linear positive operators, contraction principle, weakly Picard operators, delta operators, operators of binomial type.

Paper coordinates

O. Agratini, I.A. Rus, Iterates of a class of discrete linear operators via contraction principle, Commentationes Mathematicae Universitatis Carolinae 44 (3), 555-563


About this paper

Publisher Name
Print ISSN


Online ISSN


google scholar link

[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] Lupas A., Approximation operators of binomial type, New developments in approximation theory (Dortmund, 1998), pp. 175–198, International Series of Numerical Mathematics, Vol.132, Birkhauser 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, Babes-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. Numer. Theor. Approx. 27 (1998), no. 1, 167–181


Related Posts