About the bivariate operators of Durrmeyer-type

• Autorzy: Pop O. , Farcas M.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to study the convergence and approximation properties of the bivariate operators and GBS operators of Durrmeyer-type.

Słowa kluczowe

EN

bivariate operators; GPS operators; linear operators

PL

operatory dwuwymiarowe; operatory GPS; operatory liniowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 1
• Strony: 97--107
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Pop O.

autor

Farcas M.

• National College "Mihai Eminescu" 5 Mihai Eminescu Street Satu Mare 440014, Romania,

Bibliografia

• [1] I. Badea, Modul de continuitate in sens Bogel si unele aplica?ii in aproximarea printrun operator Bernstein, Studia Univ. Babes-Bolyai Math. 18 (2) (1973), 69-78 (Romanian).
• [2] C. Badea, I. Badea, H. H. Gonska, A test function theorem and approximation by pseudopolynomials, Bull. Austral. Math. Soc. 34 (1986), 55-64.
• [3] C. Badea, C. Cottin, Korovkin-type theorems for generalized boolean sum operators, Colloq. Math. Soc. Janos Bolyai, 58, Approximation Theory, Kecskemét (Hungary) (1990), 51-67 (1988), 95-108.
• [4] C. Badea, I. Badea, C. Cottin, H. H. Gonska, Notes on the degree of approximation of B-continuous and B-differentiable functions, J. Approx. Theory Appl. 4 (1988), 95-108.
• [5] D. Bărbosu, Polynomial Approximation by Means of Schurer-Stancu type Operators, Ed. Universităµii de Nord, Baia Mare, 2006.
• [6] K. Bögel, Mehrdimensionale Differentiation von Funtionen mehrerer Veranderlicher, J. Reine Angew. Math. 170 (1934), 197-217.
• [7] K. Bögel, Über die mehrdimensionale Differentiation, Integration und beschrankte Variation, J. Reine Angew. Math. 173 (1935), 5-29.
• [8] K. Bögel, Über die mehrdimensionale Differentiation, Jber. DMV 65 (1962), 45-71.
• [9] M. M. Derriennic, Sur l’approximation des functions integrables sur [0,1] par des polinômes de Bernstein modifies, J. Approx. Theory 31 (1981), 325-343.
• [10] J. L. Durrmeyer, Une formule d’inversion de la transformee de Laplace: Applications ? la theorie des momentes, Thése de 3e cycle, Faculté des Sciences de l’Université de Paris, 1967.
• [11] G. G. Lorentz, Bernstein Polynomials, University of Toronto Press, Toronto, 1953.
• [12] O. T. Pop, M. D. Fărcas, Approximation of B-continuous and B-differentiable functions by GBS operators of Bernstein bivariate polynomials, J. Inequal. Pure Appl. Math. 7 (2006), 9 pp. (electronic).
• [13] O. T. Pop, Approximation of B-differentiable functions by GBS operators, Anal. Univ. Oradea, Fasc. Matem. Tom XIV (2007), 15-31.
• [14] D. D. Stancu, Asupra aproximării func?iilor de două variabile prin polinoame de tip Bernstein. Cateva evaluări asimptotice, Studii si Cercetări Matematice 11 (1960), 171-176 (Romanian).
• [15] D. D. Stancu, Gh. Coman, Gh. Agratini, Gh. Trîmbiµas, Analiză numerică si teoria aproximării ?, Presa Universitară Clujeană, Cluj-Napoca, 2001 (Romanian).
• [16] A. F. Timan, Theory of Approximation of Functions of Real Variable, New York: Macmillan Co. 1963. MR22#8257.