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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 61, Issue 2

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A Voronovskaya-type formula for SMK operators via statistical convergence

Ali Aral / Oktay Duman
Published Online: 2011-04-09 | DOI: https://doi.org/10.2478/s12175-011-0008-3

Abstract

In this paper, we obtain a statistical Voronovskaya-type theorem for the Szász-Mirakjan-Kantorovich (SMK) operators by using the notion of A-statistical convergence, where A is a non-negative regular summability matrix.

MSC: Primary 41A25, 41A36

Keywords: A-statistical convergence; Szász-Mirakjan operators; Korovkin-type approximation theorem; Voronovskaya-type theorem

  • [1] ALTOMARE, F.—CAMPITI, M.: Korovkin Type Approximation Theory and Its Application. de Gruyter Stud. Math. 17, de Gruyter & Co., Berlin, 1994. Google Scholar

  • [2] ANASTASSIOU, G. A.—DUMAN, O.: A Baskakov type generalization of statistical Korovkin theory, J. Math. Anal. Appl. 340 (2008), 476–486. http://dx.doi.org/10.1016/j.jmaa.2007.08.040CrossrefGoogle Scholar

  • [3] ANASTASSIOU, G. A.—DUMAN, O.: Statistical fuzzy approximation by fuzzy positive linear operators, Comput. Math. Appl. 55 (2008), 573–580. http://dx.doi.org/10.1016/j.camwa.2007.05.007Web of ScienceCrossrefGoogle Scholar

  • [4] DUMAN, O.—ANASTASSIOU, G. A.: On statistical fuzzy trigonometric Korovkin theory, J. Comput. Anal. Appl. 10 (2008), 333–344. Google Scholar

  • [5] DUMAN, O.—ERKUŞ, E.—GUPTA, V.: Statistical rates on the multivariate approximation theory, Math. Comput. Modelling 44 (2006), 763–770. http://dx.doi.org/10.1016/j.mcm.2006.02.009CrossrefGoogle Scholar

  • [6] ERKUŞ, E.—DUMAN, O.: A Korovkin type approximation theorem in statistical sense, Studia Sci. Math. Hungar. 43 (2006), 285–294. Google Scholar

  • [7] ERKUŞ, E.—DUMAN, O.: A-Statistical extension of the Korovkin type approximation theorem, Proc. Indian Acad. Sci. Math. Sci. 115 (2005), 499–508. http://dx.doi.org/10.1007/BF02829812CrossrefGoogle Scholar

  • [8] ERKUŞ, E.—DUMAN, O.—-SRIVASTAVA, H. M.: Statistical approximation of certain positive linear operators constructed by means of the Chan-Chyan-Srivastava polynomials, Appl. Math. Comput. 182 (2006), 213–222. http://dx.doi.org/10.1016/j.amc.2006.01.090Web of ScienceCrossrefGoogle Scholar

  • [9] ERKUŞ-DUMAN, E.—DUMAN, O.: Integral-type generalizations of operators obtained from certain multivariate polynomials, Calcolo 45 (2008), 53–67. http://dx.doi.org/10.1007/s10092-008-0143-6CrossrefWeb of ScienceGoogle Scholar

  • [10] FAST, H.: Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244. Google Scholar

  • [11] FREEDMAN, A. R.—SEMBER, J. J.: Densities and summability, Pacific J. Math. 95 (1981), 293–305. Google Scholar

  • [12] FRIDY, J. A.: On statistical convergence, Analysis (Munich) 5 (1985), 301–313. Google Scholar

  • [13] GADJIEV, A. D.—EFENDIEV, R. O.—IBIKLI, E.: Generalized Bernstein Chlodowsky polynomials, Rocky Mountain J. Math. 28 (1998), 1267–1277. http://dx.doi.org/10.1216/rmjm/1181071716CrossrefGoogle Scholar

  • [14] GADJIEV, A. D.—ORHAN, C.: Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), 129–138. http://dx.doi.org/10.1216/rmjm/1030539612CrossrefGoogle Scholar

  • [15] HARDY, G. H.: Divergent Series, Oxford Univ. Press, London, 1949. Google Scholar

  • [16] KARAKUŞ, S.—DEMIRCI, K.—DUMAN, O.: Equi-statistical convergence of positive linear operators, J. Math. Anal. Appl. 339 (2008), 1065–1072. http://dx.doi.org/10.1016/j.jmaa.2007.07.050CrossrefGoogle Scholar

  • [17] KOLK, E.: Matrix summability of statistically convergent sequences, Analysis (Munich) 13 (1993), 77–83. Google Scholar

  • [18] KOROVKIN, P. P.: Linear Operators and the Theory of Approximation, Hindustan Publ. Co., Delhi, 1960. Google Scholar

  • [19] VORONOVSKAYA, E.: Determination de la forme asymtotique dáproximation des functions par les polynomes de M. Bernstein, C. R. Acad. Sci. URSS 79 (1932), 79–85. Google Scholar

About the article

Published Online: 2011-04-09

Published in Print: 2011-04-01


Citation Information: Mathematica Slovaca, Volume 61, Issue 2, Pages 235–244, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-011-0008-3.

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© 2011 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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