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Voronovskaja-type theorems and approximation theorems for a class of GBS operators

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EN
In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through parti- cular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, Bleimann- Butzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.
Rocznik
Tom
Strony
91--108
Opis fizyczny
Bibliogr. 36 poz.
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autor
Bibliografia
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  • [3] Baskakov V.A., An example of a sequence of linear positive operators in the space of continuous functions, Dokl. Acad. Nauk, SSSR, 113(1957), 249-251.
  • [4] Bărbosu D., Voronovskaja theorem for Bernstein-Schurer bivariate operator, Rev. Anal. Numér. Théor. Approx., 33(1)(2004), 19-24.
  • [5] Bernstein S.N., Démonstration du théoreme de Weierstrass fondée sur le calcul de probabilités, Commun. Soc. Math. Kharkow (2), 13(1912-1913), 1-2.
  • [6] Becker M., Nessel R.J., A global approximation theorem for Meyer-König and Zeller operators, Math. Zeitschr., 160(1978), 195-206.
  • [7] Bleimann G., Butzer P.L., Hahn L., A Bernstein-type operator approximating continuous functions on the semi-axis, Indag. Math., 42(1980), 255-262.
  • [8] Cheney E.W., Sharma A., Bernstein power series, Canadian J. Math., 16(2)(1964), 241-252.
  • [9] Derriennic M.M., Sur l’approximation des fonctions intégrables sur [0, 1] par des polynômes de Bernstein modifiés, J. Approx. Theory, 31(1981), 325-343.
  • [10] DeVore R.A., Lorentz G.G., Constructive approximation, Springer Verlag, Berlin, Heidelberg, New York, 1993.
  • [11] Durrmeyer J.L., Une formule d’inversion de la transformée de Laplace: Applications à la théorie des moments, Thèse de 3e cycle, Faculté des Sciences de l’Université de Paris 1967.
  • [12] Favard J., Sur les multiplicateurs d’interpolation, J. Math. Pures Appl., 23(9)(1944), 219-247.
  • [13] Ismail M., May C.P., On a family of approximation operators, J. Math. Anal. Appl., 63(1978), 446-462.
  • [14] Kantorovich L.V., Sur certain développements suivant les polynômes de la forme de S. Bernstein, C. R. Acad. URSS, 1(2)(1930), 563-568, 595-600.
  • [15] Lorentz G.G., Bernstein polynomials, University of Toronto Press, Toronto, 1953.
  • [16] Lorentz G.G., Approximation of functions, Holt, Rinehart and Winston, New York, 1966.
  • [17] Meyer-König W., Zeller K., Bernsteinsche potenzreihen, Studia Math., 19(1960), 89-94.
  • [18] Mirakjan G.M., Approximation of continuous functions with the aid of polynomials, Dokl. Acad. Nauk SSSR, 31(1941), 201-205 (Russian).
  • [19] Müller M.W., Die Folge der Gammaoperatoren, Dissertation, Stuttgart, 1967.
  • [20] Pop O.T., New properties of the Bernstein-Stancu operators, Anal. Univ. Oradea, Fasc. Matematica, 11(2004), 51-60.
  • [21] Pop O.T., The generalization of Voronovskaja’s theorem for a class of linear and positive operators, Rev. Anal. Num. Théor. Approx., 34(1)(2005), 79-91.
  • [22] Pop O.T., About a general property for a class of linear positive operators and applications, Rev. Anal. Num. Théor. Approx., 34(2)(2005), 175-180.
  • [23] Pop O.T., About some linear and positive operators defined by infinite sum, Dem. Math., 39(2)(2006), 377-388.
  • [24] Pop O.T., About a class of linear and positive operators, Carpathian J. Math., 21(1-2)(2005), 99-108.
  • [25] Pop O.T., The generalization of Voronovskaja’s theorem for a class of bivariate operators defined by infinite sum, Anal. Univ. Oradea, Fasc. Matematica, 15(2008), 155-169.
  • [26] Pop O.T., The generalization of Voronovskaja’s theorem for exponential operators, Creative Math.& Inf., 16(2007), 54-62.
  • [27] Pop O.T., The Voronovskaja type theorem for the Stancu bivariate operators, Austral. J. Math. Anal. and Appl., 3(2)(2006), Art. 10, 9 pp. (electronic).
  • [28] Pop O.T., About operator of Bleimann, Butzer and Hahn, Anal. Univ. Timişoara, XLIII, Fasc. 1 (2005), 117-127.
  • [29] Pop O.T., The generalization of Voronovskaja’s theorem for a class of bivariate operators, Univ. ”Babes-Bolyai”, Mathematica, 53(2)(2008), 85-107.
  • [30] Pop O.T., Voronovskaja-type theorem for certain GBS operators, Glasnik Matematicki, 43(63)(2008), 179-194.
  • [31] Schurer F., Linear positive operators in approximation theory, Math. Inst. Techn., Univ. Delft. Report, 1962.
  • [32] Stancu D.D., Asupra unei generaliări a polinoamelor lui Bernstein, Studia Univ. Babeş-Bolyai, Ser. Math.-Phys., 14(1969), 31-45 (Romanian).
  • [33] Stancu D.D., Coman Gh., Agratini O., Trîmbiţaş R., Analiză numerică şi teoria aproximării, I, Presa Universitară Clujeană, Cluj-Napoca, 2001 (Romanian).
  • [34] Szász O., Generalization of S. Bernstein’s polynomials to the infinite interval, J. Research, National Bureau of Standards, 45(1950), 239-245.
  • [35] Timan A.F., Theory of Approximation of Functions of Real Variable, New York: Macmillan Co. 1963, MR22#8257.
  • [36] Voronovskaja E., Détermination de la forme asymptotique d’approximation des fonctions par les polynômes de M. Bernstein, C. R. Acad. Sci. URSS (1932), 79-85.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP3-0002-0056
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