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Year 2024, Volume: 16 Issue: 2, 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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  • 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.

On Bivariate Complex Schurer-type Stancu Operators

Year 2024, Volume: 16 Issue: 2, 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 Volume: 16 Issue: 2

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.