Iterates of some bivariate approximation process via weakly Picard operators


In the present paper we introduce a general class of positive operators of discrete type acting on the space of real valued functions defined on a plane domain. Based on the weakly Picard operators and the contraction principle as well, our aim is to study the convergence of the iterates of our defined operators. Also, some approximation properties of this process are revealed and concrete examples of our approach are given.


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


Approximation process, contraction principle, weakly Picard operators, first-order modulus of continuity.

Paper coordinates

O. Agratini, I.A. Rus, Iterates of some bivariate approximation process via weakly Picard operators, Nonlinear Analysis Forum, 8 (2003), pp. 159-168.


About this paper


Nonlinear Analysis Forum

Publisher Name
Print ISSN


Online ISSN


google scholar link

[1] F. Altomare and M. Campiti, Korovkin-type Approximation Theory and its Applications, Vol. 17, Walter de Gruyter Studies in Mathematics, Berlin-New York, 1994.
[2] I. Badea, The modulus of oscillation for functions of two variables and some applications in the approximation by Bernstein operator, (in Romanian), An. Univ. Craiova, Series V. 2 (1974), 43–54.
[3] A. F. Ipatov, Estimate of the error and order of approximation of functions of two variables by S. N. Bernstein’s polynomials, (in Russian), U˘c. Zap. Petrozavodsk Univ., 4(4) (1955), 31–48.
[4] I. A. Rus,, Weakly Picard mappings, Commentationes Math. Univ Carolinae, 34(4) (1993), 769–773.
[5] , Generalized Contractions and Applications, University Press, Cluj-Napoca, 2001.
[6] P. C. Sikkema, Der Wert einiger Konstanten in der theorie der approximation mit Bernstein Polynomen, Numer. Math. 3 (1961), 107–116.
[7] D. D. Stancu, Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures et Appl., 13(8) (1968), 1173–1194.


Related Posts