## Abstract

The present paper focuses on two approaches. Firstly, by using the contraction principle, we give a method for obtaining the limit of iterates of a class of linear positive operators. This general method is applied in studying three sequences of modified Bernstein type operators. Secondly, we define a generalization of Goodman-Sharma operators. We investigate the degree of approximation obtaining pointwise and global estimates in the framework of various function spaces.

## Authors

**Octavian Agratini**

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

## Keywords

linear positive operators; contraction principle; degree of approximation; modulus of smoothness.

## Paper coordinates

O. Agratini, *On some Bernstein type operators: iterates and generalizations*, East Journal on Approximations, **9** (2003) no. 4, pp. 415-426.

## About this paper

##### Journal

East Journal on Approximations

##### Publisher Name

##### DOI

##### Print ISSN

??

##### Online ISSN

google scholar link

[1] M. Campiti and G. Metafune, *Approximation properties of recursively defined Bernstein-type operators, * J. Approx. Theory 87 (1996), pp. 243-269.

[2] E.W. Cheney and A. Sharma, * On a generalization of Bernstein polynomials, * Riv. Mat. Univ. Parma (2) 5 (1964), pp. 77-84.

[3] M.M. Derroemmoc, * Sur l’approximation de fonctions integrables sur [0,1] par des polynomes de Bernstein modifies, * J.Approx. Theory 31 (1981), pp.325-343.

[4] T.N.T. Goodman and A. Sharma, * A Bernstein-type operator on the simplex, * Math. Balkanica (N.S) 5 (1991), f.2, pp.129-145.

[5] R.P.Kelisky and T.J. Rivlin, *Iterates of Bernstein polynomials, *Pacific J. Math. 21 (1967(, pp. 511-520.

[6] I.A. Rus, * Weakly Picard mappings, * Commentationes Math. Univ. Carolinae 34, 4 (1993), pp. 769-773.

[7] D.D. Stancu, *Approximation of functions by means of a new generalized Bernstein operator, * Calcolo, 20 (1983), f.2, pp.211-229.

[8] D.D. Stancu and C.Cismasiu, * On an approximating linear positive operator of Cheney-Sharma, * Revue d’Analyse Numerique et de Theorie de l’Approximation, 26 (1997), no.1-2, pp. 221-227.