Research Article
BibTex RIS Cite

GBS Operators of Bivariate Durrmeyer Operators on Simplex

Year 2021, Volume: 4 Issue: 2, 108 - 114, 30.06.2021
https://doi.org/10.33434/cams.932416

Abstract

We define GBS operators of Durrmeyer operators for bivariate functions on simplex and we give their approximations and rate of their approximations for B-continuous and B-differentiable functions. We show that the GBS type the operators of new Durrmeyer have better approximation than the new operators.

References

  • [1] J. L. Durrmeyer, "une formule d′ inversion de la transformee de Laplace:Applicationsa la theorie de moments", these de′ 3e cycle, Faculte des sciences de 1 universite de Paris,1967.
  • [2] M. M. Derriennic,Sur l′ approximation de fonctions integrables sur [0, 1] par de polynomes de Bernstein modifies, J. Approx. Theory, 31(1981),325-343.
  • [3] S.P. Singh,On approximation Of Integrable Functions By Modified Bernstein Polynomials, Publications De L’Institut Mathematicque, 41(55), (1987), 91-95.
  • [4] K. Bögel,Mehrdimensionale Differentitation von Funktionen mehrerer Veranderhicher, J. Reine agnew. Math., 170, (1934) 197-217.
  • [5] K. Bögel,Uber die mehrdimensionale Differentitation, Integration and beschra ̈nkte variation , J. Reine agnew. Math., (1935) 173, 5-29.
  • [6] K. Bögel,Uber die mehrdimensionale Differentitation, Jber. DMV, 65, (1962) 45-71.
  • [7] E. Dobrescu, I. Matei,Approximarea prin polinoame de tip Bernstein a functiilor bidimensional continue, Anal. Univ. Timisoara , Seria Stiinte matematici-fizice, IV (1966), 85-90.
  • [8] C. Badea, I.Badea, H. H. Gonska,A test function theorem and approximation by pseudopolynomials, Bull. Austral. Math. Soc.,34, (1986) 53-64.
  • [9] I. Badea, Modul de continuitate in sens Bo ̈gel s ̧i unele applicatii in approximarea printr-un operator Bernstein, Studia Univ. ”Babes ̧-Bolyai” Ser. Math-Mech., 18(2), (1973)69-78, (Romanian).
  • [10] H. H. Gonska,Quantitative approximation in C(X), Habilitationsschrift, Universitaa ̈t Disburg, (1985).
  • [11] C. Badea, C. Cottin, Korovkin-type theorems for Generalized Boolean Sum operators, Colloquia Mathematica Sociekatis Janos Bolyai, 58, Approximation Theory , Kecskemet(Hungary), (1990) 51-68.
  • [12] V. Volkov, I.On the convergence of sequences of linear positive operators in the space of continuous functions of two variable, Math. Sb. N. S. 43(85) (1957) 504 (Russian).
  • [13] O. T. Pop,Approximation of B-differentiable functions by GBS operators, Analele Univ. Oradea. Fac. Mathematica, Tom. XIV, (2007) 15-31.
Year 2021, Volume: 4 Issue: 2, 108 - 114, 30.06.2021
https://doi.org/10.33434/cams.932416

Abstract

References

  • [1] J. L. Durrmeyer, "une formule d′ inversion de la transformee de Laplace:Applicationsa la theorie de moments", these de′ 3e cycle, Faculte des sciences de 1 universite de Paris,1967.
  • [2] M. M. Derriennic,Sur l′ approximation de fonctions integrables sur [0, 1] par de polynomes de Bernstein modifies, J. Approx. Theory, 31(1981),325-343.
  • [3] S.P. Singh,On approximation Of Integrable Functions By Modified Bernstein Polynomials, Publications De L’Institut Mathematicque, 41(55), (1987), 91-95.
  • [4] K. Bögel,Mehrdimensionale Differentitation von Funktionen mehrerer Veranderhicher, J. Reine agnew. Math., 170, (1934) 197-217.
  • [5] K. Bögel,Uber die mehrdimensionale Differentitation, Integration and beschra ̈nkte variation , J. Reine agnew. Math., (1935) 173, 5-29.
  • [6] K. Bögel,Uber die mehrdimensionale Differentitation, Jber. DMV, 65, (1962) 45-71.
  • [7] E. Dobrescu, I. Matei,Approximarea prin polinoame de tip Bernstein a functiilor bidimensional continue, Anal. Univ. Timisoara , Seria Stiinte matematici-fizice, IV (1966), 85-90.
  • [8] C. Badea, I.Badea, H. H. Gonska,A test function theorem and approximation by pseudopolynomials, Bull. Austral. Math. Soc.,34, (1986) 53-64.
  • [9] I. Badea, Modul de continuitate in sens Bo ̈gel s ̧i unele applicatii in approximarea printr-un operator Bernstein, Studia Univ. ”Babes ̧-Bolyai” Ser. Math-Mech., 18(2), (1973)69-78, (Romanian).
  • [10] H. H. Gonska,Quantitative approximation in C(X), Habilitationsschrift, Universitaa ̈t Disburg, (1985).
  • [11] C. Badea, C. Cottin, Korovkin-type theorems for Generalized Boolean Sum operators, Colloquia Mathematica Sociekatis Janos Bolyai, 58, Approximation Theory , Kecskemet(Hungary), (1990) 51-68.
  • [12] V. Volkov, I.On the convergence of sequences of linear positive operators in the space of continuous functions of two variable, Math. Sb. N. S. 43(85) (1957) 504 (Russian).
  • [13] O. T. Pop,Approximation of B-differentiable functions by GBS operators, Analele Univ. Oradea. Fac. Mathematica, Tom. XIV, (2007) 15-31.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Harun Çiçek

Aydın İzgi

Mehmet Ayhan

Publication Date June 30, 2021
Submission Date May 4, 2021
Acceptance Date June 28, 2021
Published in Issue Year 2021 Volume: 4 Issue: 2

Cite

APA Çiçek, H., İzgi, A., & Ayhan, M. (2021). GBS Operators of Bivariate Durrmeyer Operators on Simplex. Communications in Advanced Mathematical Sciences, 4(2), 108-114. https://doi.org/10.33434/cams.932416
AMA Çiçek H, İzgi A, Ayhan M. GBS Operators of Bivariate Durrmeyer Operators on Simplex. Communications in Advanced Mathematical Sciences. June 2021;4(2):108-114. doi:10.33434/cams.932416
Chicago Çiçek, Harun, Aydın İzgi, and Mehmet Ayhan. “GBS Operators of Bivariate Durrmeyer Operators on Simplex”. Communications in Advanced Mathematical Sciences 4, no. 2 (June 2021): 108-14. https://doi.org/10.33434/cams.932416.
EndNote Çiçek H, İzgi A, Ayhan M (June 1, 2021) GBS Operators of Bivariate Durrmeyer Operators on Simplex. Communications in Advanced Mathematical Sciences 4 2 108–114.
IEEE H. Çiçek, A. İzgi, and M. Ayhan, “GBS Operators of Bivariate Durrmeyer Operators on Simplex”, Communications in Advanced Mathematical Sciences, vol. 4, no. 2, pp. 108–114, 2021, doi: 10.33434/cams.932416.
ISNAD Çiçek, Harun et al. “GBS Operators of Bivariate Durrmeyer Operators on Simplex”. Communications in Advanced Mathematical Sciences 4/2 (June 2021), 108-114. https://doi.org/10.33434/cams.932416.
JAMA Çiçek H, İzgi A, Ayhan M. GBS Operators of Bivariate Durrmeyer Operators on Simplex. Communications in Advanced Mathematical Sciences. 2021;4:108–114.
MLA Çiçek, Harun et al. “GBS Operators of Bivariate Durrmeyer Operators on Simplex”. Communications in Advanced Mathematical Sciences, vol. 4, no. 2, 2021, pp. 108-14, doi:10.33434/cams.932416.
Vancouver Çiçek H, İzgi A, Ayhan M. GBS Operators of Bivariate Durrmeyer Operators on Simplex. Communications in Advanced Mathematical Sciences. 2021;4(2):108-14.

Creative Commons License
The published articles in CAMS are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License..