## Abstract

We consider some Cheney-Sharma type operators as well as their product and Boolean sum for a function defined on a triangle with one curved side.

Using the weakly Picard operators technique and the contraction principle, we study the convergence of the iterates of these operators.

## Authors

**Teodora Cătinaș**

Babes-Bolyai University, Cluj Napoca, Romania

**Diana Otrocol**

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Technical University of Cluj Napoca, Romania

## Keywords

Triangle with curved side; Cheney-Sharma operators; contraction principle; weakly Picard operators

### References

See the expanding block below.

## Paper coordinates

T. Cătinaș, D. Otrocol, *Iterates of Cheney-Sharma type operators on a triangle with curved* side, Journal Computational Analysis and Applications, 28 (2020) no. 4, pp. 737-744.

## About this paper

##### Journal

Journal Computational Analysis and Applications

##### Publisher Name

Eudoxus Press, LLC ?

##### DOI

##### Print ISSN

1521-1398

##### Online ISSN

##### Google Scholar Profile

google scholar

[1] Agratini, O., Rus, I.A., Iterates of a class of discrete linear operators via contraction principle, Comment. Math. Univ. Caroline 44 (2003), 555-563.

[2] Agratini, O., Rus, I.A., Iterates of some bivariate approximation process via weakly Picard operators, Nonlinear Anal. Forum 8(2) (2003), 159-168.

[3] Blaga, P., Catinas, T., Coman, G., Bernstein-type operators on triangle with one curved side, Mediterr. J. Math. 9 (2012), No. 4, 833-845.

[4] Blaga, P., Catinas, T., Coman, G., Bernstein-type operators on a square with one and two curved sides, Studia Univ. Babe¸s–Bolyai Math. 55 (2010), No. 3, 51-67.

[5] Blaga, P., C˘atina¸s, T., Coman, G., Bernstein-type operators on triangle with all curved sides, Appl. Math. Comput. 218 (2011), 3072-3082.

[6] Catinas, T., Extension of some Cheney-Sharma type operators to a triangle with one curved side, 2017, submitted.

[7] Catinas, T., Otrocol, D., Iterates of Bernstein type operators on a square with one curved side via contraction principle, Fixed Point Theory 14 (2013), No. 1, 97-106.

[8] Catinas, T., Otrocol, D., Iterates of multivariate Cheney-Sharma operators, J. Comput. Anal. Appl. 15 (2013), No. 7, 1240-1246.

[9] Coman, G., Catinas, T., Interpolation operators on a triangle with one curved side, BIT Numerical Mathematics 50 (2010), No. 2, 243-267.

[10] Gavrea, I., Ivan, M., The iterates of positive linear operators preserving the affine functions, J. Math. Anal. Appl. 372 (2010), 366-368.

[11] Gavrea, I., Ivan, M., The iterates of positive linear operators preserving the constants, Appl. Math. Lett. 24 (2011), No. 12, 2068-2071.

[12] Gavrea, I., Ivan, M., On the iterates of positive linear operators, J. Approx. Theory 163 (2011), No. 9, 1076-1079.

[13] Gonska, H., Kacso, D., Pitul, P., The degree of convergence of over-iterated positive linear operators, J. Appl. Funct. Anal. 1 (2006), 403-423.

[14] Gonska, H., Pitul, P., Rasa, I., Over-iterates of Bernstein-Stancu operators, Calcolo 44 (2007), 117-125.

[15] Gonska, H., Rasa, I., The limiting semigroup of the Bernstein iterates: degree of convergence, Acta Math. Hungar. 111 (2006), No. 1-2, 119-130.

[16] Gonska, H., Ra¸sa, I., On infinite products of positive linear operators reproducing linear functions, Positivity 17 (2013), No. 1, 67-79.

[17] Gwozdz- Lukawska, G., Jachymski, J., IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem, J. Math. Anal. Appl. 356(2) (2009), 453-463.

[18] Karlin, S. , Ziegler, Z., Iteration of positive approximation operators, J. Approx. Theory 3 (1970), 310-339.

[19] Kelisky, R.P., Rivlin, T.J., Iterates of Bernstein polynomials, Pacific J. Math. 21 (1967), 511-520.

[20] Rasa, I., C0-Semigroups and iterates of positive linear operators: asymptotic behaviour, Rend. Circ. Mat. Palermo, Ser. II, Suppl. 82 (2010), 123-142.

[21] Rus, I.A., Picard operators and applications, Sci. Math. Jpn. 58 (2003), 191-219.

[22] Rus, I.A., Iterates of Stancu operators, via contraction principle, Studia Univ. Babes–Bolyai Math. 47 (2002), No. 4, 101-104.

[23] Rus, I.A., Iterates of Bernstein operators, via contraction principle, J. Math. Anal. Appl. 292 (2004), 259-261.

[24] Rus, I.A., Fixed point and interpolation point set of a positive linear operator on C(D), Studia Univ. Babes–Bolyai Math. 55 (2010), No. 4, 243-248.