GBS Operators of Bivariate Durrmeyer Operators on Simplex

Year 2021, Volume: 4 Issue: 2, 108 - 114, 30.06.2021

Harun Çiçek , Aydın İzgi , Mehmet Ayhan

https://doi.org/10.33434/cams.932416

Cited By: 1

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.

Keywords

Durrmeyer operators on simplex , GBS-operators , Bivariate 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.