Abstract
The study focuses on the approximation features of the bivariate generalization of the complex Schurer form of Stancu-type operators. We have obtained a Voronovskaja type solution that provides quantitative estimates for bivariate complex operators coupled to analytic functions. Furthermore, the exact order of approximation is provided.
Keywords
bivariate complex opertators Schurer-type Stancu operators rate of convergence exact order.
References
- Acar, T., Aral, A., Approximation properties of two dimensional Bernstein-Stancu-Chlodowsky operators, Le Matematiche 68(2)(2013), 15–31.
- Bozkurt, K., Özsaraç, F., Aral, A., Bivariate Bernstein polynomials that reproduce exponential functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.,70(1)(2021), 541–554.
- Çetin, N., A new generalization of complex Stancu operators, Mathematical Methods in the Applied Sciences, 42(2019), 5582–5594.
- Çetin, N., Başcanbaz-Tunca, G., Approximation by a new complex generalized Bernstein operator, An. Univ. Oradea Fasc. Mat. 26(2)(2019), 129–141.
- Çetin, N., A new complex generalized Bernstein-Schurer operator, Carpathian J. Math., 37(1)(2021), 81–89.
- Çetin, N., Manav Mutlu, N., Complex generalized Stancu-Schurer operators, Mathematica Slovaca, 74(5)(2024), 1215–1232.
- Gal, S.G., Approximation by Complex Bernstein and Convoluation Type Operators, World Scientific, Sigapore, 2009.
- Gal, S.G., Approximation by Complex Bernstein and Convolution Type Operators, Series on Concrete and Applicable Mathematics, 8. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, USA, 2009.
- Manav Mutlu, N., On new bivariate Schurer-Stancu-type operators, (submitted).
- Özden, D.S., Arı, D.A., Approximation by a complex q-Baskakov-Stancu operator in compact disks, Journal of Inequalities and Applications, (2014), 1–15.
- Paltanea, R., Durrmeyer type operators on a simplex, Constructive Mathematical Analysis, 4(2)(2021), 215–228.
- Stancu, D.D., Approximation of functions by means of a new generalized Bernstein operator, Calcolo, 20(1983), 211–229.
- Stancu, D.D., Quadrature formulas constructed by using certain linear positive operators, Numerical Integration (Proc. Conf., Oberwolfach,1981), 57(1982), 241–251.
- Stancu, D.D., Approximation of functions by means of a new generalized Bernstein operator, Calcolo, 20(1983) 211–229.
- Yang, R., Xiong, J., Cao, F., Multivariate Stancu operators defined on a simplex, Appl. Math. Comput., 138(2003), 189–198.
Abstract
References
- Acar, T., Aral, A., Approximation properties of two dimensional Bernstein-Stancu-Chlodowsky operators, Le Matematiche 68(2)(2013), 15–31.
- Bozkurt, K., Özsaraç, F., Aral, A., Bivariate Bernstein polynomials that reproduce exponential functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.,70(1)(2021), 541–554.
- Çetin, N., A new generalization of complex Stancu operators, Mathematical Methods in the Applied Sciences, 42(2019), 5582–5594.
- Çetin, N., Başcanbaz-Tunca, G., Approximation by a new complex generalized Bernstein operator, An. Univ. Oradea Fasc. Mat. 26(2)(2019), 129–141.
- Çetin, N., A new complex generalized Bernstein-Schurer operator, Carpathian J. Math., 37(1)(2021), 81–89.
- Çetin, N., Manav Mutlu, N., Complex generalized Stancu-Schurer operators, Mathematica Slovaca, 74(5)(2024), 1215–1232.
- Gal, S.G., Approximation by Complex Bernstein and Convoluation Type Operators, World Scientific, Sigapore, 2009.
- Gal, S.G., Approximation by Complex Bernstein and Convolution Type Operators, Series on Concrete and Applicable Mathematics, 8. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, USA, 2009.
- Manav Mutlu, N., On new bivariate Schurer-Stancu-type operators, (submitted).
- Özden, D.S., Arı, D.A., Approximation by a complex q-Baskakov-Stancu operator in compact disks, Journal of Inequalities and Applications, (2014), 1–15.
- Paltanea, R., Durrmeyer type operators on a simplex, Constructive Mathematical Analysis, 4(2)(2021), 215–228.
- Stancu, D.D., Approximation of functions by means of a new generalized Bernstein operator, Calcolo, 20(1983), 211–229.
- Stancu, D.D., Quadrature formulas constructed by using certain linear positive operators, Numerical Integration (Proc. Conf., Oberwolfach,1981), 57(1982), 241–251.
- Stancu, D.D., Approximation of functions by means of a new generalized Bernstein operator, Calcolo, 20(1983) 211–229.
- Yang, R., Xiong, J., Cao, F., Multivariate Stancu operators defined on a simplex, Appl. Math. Comput., 138(2003), 189–198.
Details
| Primary Language | English |
|---|---|
| Subjects | Approximation Theory and Asymptotic Methods |
| Journal Section | Research Article |
| Authors | |
| Submission Date | April 12, 2024 |
| Acceptance Date | December 1, 2024 |
| Publication Date | December 31, 2024 |
| Published in Issue | Year 2024 Volume: 16 Issue: 2 |