Abstract
In this paper, we study an extension of the bivariate Lupaş–Durrmeyer operators based on Polya distribution. For these operators we get a Voronovskaja type theorem and the order of approximation using Peetre’s K-functional. Then, we construct the Generalized Boolean Sum operators of Lupaş–Durrmeyer type and estimate the degree of approximation in terms of the mixed modulus of smoothness.
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Agrawal P.N., Ispir N., Kajla A.: Approximation properties of Lupaş–Kantorovich operators based on Polya distribution, Rend. Circ. Mat. Palermo. (submitted)
Badea C.: K-functionals and moduli of smoothness of functions defined on compact metric spaces. Comput. Math. Appl. 30, 23–31 (1995)
Badea C., Badea I., Cottin C., Gonska H.H.: Notes on the degree of approximation of B-continuous and B-differentiable functions. Approx. Theory Appl. 4, 95–108 (1988)
Badea C., Badea I., Gonska H.H.: A test function theorem and approximation by pseudopolynomials. Bull. Aust. Math. Soc. 34, 53–64 (1986)
Badea C., Cottin C.: Korovkin-Type Theorems for Generalized Boolean Sum Operators, Approximation Theory (Kecskemét 1900), Colloq. Math. Soc. János Bolyai, North-Holland, Amsterdam, 58, 51–68 (1990)
Bǎrbosu D., Muraru C.V.: Approximating B-continuous functions using GBS operators of Bernstein–Schurer–Stancu type based on q-integers. Appl. Math. Comput. 259, 80–87 (2015)
Bögel K.: Mehrdimensionale Differentiation von Funktionen mehrerer reeller Veränderlichen. J. Reine Angew. Math. 170, 197–217 (1934)
Bögel K.: Über die mehrdimensionale differentiation, integration und beschränkte variation. J. Reine Angew. Math. 173, 5–29 (1935)
Bögel K.: Über die mehrdimensionale differentiation. Jber. Dtsch. Math. Verein. 65, 45–71 (1962–1963)
Cottin C.: Mixed K-functionals: a measure of smoothness for blending-type approximation. Math. Z. 204, 69–83 (1990)
Dobrescu E., Matei I.: The approximation by Bernstein type polynomials of bidimensionally continuous functions, (Romanian). Ann. Univ. Timiş. Ser. Şti. Mat. Fiz. 4, 85–90 (1966)
Gonska, H.H.: Quantitative Approximation in C(X). Habilitationsschrift, Universita at Duisburg (1985)
Gupta V., Rassias T.M.: Lupaş–Durrmeyer operators based on Polya distribution. Banach J. Math. Anal. 8(2), 146–155 (2014)
Lupaş L., Lupaş A.: Polynomials of binomial type and approximation operators. Studia Univ. Babeş-Bolyai Math. 32(4), 61–69 (1987)
Miclǎuş D.: The revision of some results for Bernstein–Stancu type operators. Carpath. J. Math. 28(2), 289–300 (2012)
Miclǎuş D.: On the GBS Bernstein–Stancu’s type operators. Creat. Math. Inform. 22, 73–80 (2013)
Pop O.T.: Approximation of B-differentiable functions by GBS operators. Anal. Univ. Oradea Fasc. Mat. 14, 15–31 (2007)
Pop O.T., Bǎrbosu D.: GBS operators of Durrmeyer–Stancu type. Miskolc. Math. Notes 9, 53–60 (2008)
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Agrawal, P.N., Ispir, N. & Kajla, A. GBS Operators of Lupaş–Durrmeyer Type Based on Polya Distribution. Results. Math. 69, 397–418 (2016). https://doi.org/10.1007/s00025-015-0507-6
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DOI: https://doi.org/10.1007/s00025-015-0507-6