Research Article
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Year 2024, , 490 - 497, 31.12.2024
https://doi.org/10.47000/tjmcs.1433508

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.
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  • Çetin, N., A new complex generalized Bernstein-Schurer operator, Carpathian J. Math., 37(1)(2021), 81–89.
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  • 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.

On Bivariate Complex Schurer-type Stancu Operators

Year 2024, , 490 - 497, 31.12.2024
https://doi.org/10.47000/tjmcs.1433508

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.

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.
There are 15 citations in total.

Details

Primary Language English
Subjects Approximation Theory and Asymptotic Methods
Journal Section Articles
Authors

Nesibe Manav Mutlu 0000-0002-7853-6337

Publication Date December 31, 2024
Submission Date April 12, 2024
Acceptance Date December 1, 2024
Published in Issue Year 2024

Cite

APA Mutlu, N. M. (2024). On Bivariate Complex Schurer-type Stancu Operators. Turkish Journal of Mathematics and Computer Science, 16(2), 490-497. https://doi.org/10.47000/tjmcs.1433508
AMA Mutlu NM. On Bivariate Complex Schurer-type Stancu Operators. TJMCS. December 2024;16(2):490-497. doi:10.47000/tjmcs.1433508
Chicago Mutlu, Nesibe Manav. “On Bivariate Complex Schurer-Type Stancu Operators”. Turkish Journal of Mathematics and Computer Science 16, no. 2 (December 2024): 490-97. https://doi.org/10.47000/tjmcs.1433508.
EndNote Mutlu NM (December 1, 2024) On Bivariate Complex Schurer-type Stancu Operators. Turkish Journal of Mathematics and Computer Science 16 2 490–497.
IEEE N. M. Mutlu, “On Bivariate Complex Schurer-type Stancu Operators”, TJMCS, vol. 16, no. 2, pp. 490–497, 2024, doi: 10.47000/tjmcs.1433508.
ISNAD Mutlu, Nesibe Manav. “On Bivariate Complex Schurer-Type Stancu Operators”. Turkish Journal of Mathematics and Computer Science 16/2 (December 2024), 490-497. https://doi.org/10.47000/tjmcs.1433508.
JAMA Mutlu NM. On Bivariate Complex Schurer-type Stancu Operators. TJMCS. 2024;16:490–497.
MLA Mutlu, Nesibe Manav. “On Bivariate Complex Schurer-Type Stancu Operators”. Turkish Journal of Mathematics and Computer Science, vol. 16, no. 2, 2024, pp. 490-7, doi:10.47000/tjmcs.1433508.
Vancouver Mutlu NM. On Bivariate Complex Schurer-type Stancu Operators. TJMCS. 2024;16(2):490-7.