About some linear and positive operators defined by infinite sum

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

Abstrakty

EN

In [13], we study a class of linear and positive operators defined by finite sum. In this paper we demonstrate general properties for a class of linear positive operators denned by infinite sum. By particularization, we obtain statements, the convergence and the evaluation for the rate of convergence in therm of the first modulus of smoothness for the Mirakjan-Favard-Szasz operators, Baskakov operators and Mayer-Konig and Zeiler operators. We don't study the convergence of these operators with the well known theorem of Bohman-Korowkin.

Słowa kluczowe

PL

operatory; operatory Baskakova; operatory Meyer-Koniga; operatory Mirakjan-Favard-Szasz; teoria Voronovskaja

EN

operators; Baskakov operators; Meyer-Konig operators; Mirakjan-Favard-Szasz operators; Voronovskaja-type theorem

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 2
• Strony: 377-388
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Pop, O.

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

Bibliografia

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• [2] V. A. Baskakov, An example of a sequence of linear positiv operators in the space of continuous functions, Dokl. Acad. Nauk, SSSR, 113 (1957), 249-251.
• [3] M. Becker, R. J. Nessel, A global approximation theorem for Meyer-Köig and Zeller operators, Math. Zeitschr., 160 (1978), 195-206.
• [4] E. W. Cheney, A. Sharma, Bernstein power series, Canadian J. Math. 16 (1964), 2, 241-252.
• [5] Z. Ditzian, V. Totik, Moduli of Smoothness, Springer Verlag, Berlin, 1987
• [6] J. Favard, Sur les multiplicateurs d'interpolation, J.Math. Pures Appl. 23(9) (1944), 219-247.
• [7] G. G. Lorent z, Bernstein Polynomials, University of Toronto Press, Toronto, 1953.
• [8] G. G. Lorent z, Approximation of Functions, Holt, Rinehart and Winston, New York, 1966.
• [9] W. Meyer -König, K. Zeller, Bernsteinsche Potenzreihen, Studia Math. 19 (1960), 89-94.
• [10] G. M. Mirakjan, Approximation of continuous functions with the aid of polynomials, Dokl. Acad. Nauk SSSR, 31 (1941), 201-205 (Russian).
• [11] M. W. Müller, Die Folge der Gammaoperatoren, Dissertation, Stuttgart, 1967.
• [12] O. T. Pop, About a class of linear and positive operators, Carpathian J. Math. 21 (2005), no. 1-2, 99-108.
• [13] O. T. Pop, The generalization of Voronovskaja's theorem for a class of linear and positive operators, Rev. Anal. Num. Th´eor. Approx. 34 (2005), no. 1, 79-91.
• [14] D. D. Stancu, Gh. Coman, O. Agrat ini, R. Trîmbiţaş, Analiză numerică ¸şi teoria aproximării , I, Presa Universitară Clujeană, Cluj-Napoca, 2001 (Romanian).
• [15] O. Szász, Generalization of S. N. Bernstein's polynomials to the infinite interval , J. Research, National Bureau of Standards 45 (1950), 239-245.
• [16] E. Voronovskaja, D´etermination de la forme asymtotique d'approximation des functions par les polynôme de Bernstein, C. R. Acad. Sci. URSS (1932), 79-85.