Approximation properties of Bernstein-Kantorovich type operators of two variables

In this study, the generalized Bernstein-Kantorovich type operators

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  • Bernstein, S. N., Demonstration du theorem de Weierstrass fondee sur le calculu des probabilites,Comp. Comm. Soc. Mat. Charkow Ser., 13(2)(1912), 1-2.
  • Korovkin, P. P., On convergence of linear positive operators in the space of continuousfunctions, Dokl. Akad. Nauk, 90(1953), 961-964.
  • Kantorovich, L. V., Sur certains developments suivant les polynomes de la forms de S.Bernstein I, II, Dokal Akad Nauk SSSR, (1930) 595-600, 563-568.
  • Durrmeyer, J. L., Une formula d’invension de la transforms de Laplace-Appliction a’la theorie des moments, The’se de 3e cycle, Faculte’ des Sciences de I’Universite de Paris, (1967).
  • Izgi, A., Approximation by a class of new type Bernstein polynomials of one two variables,Global Journal of Pure and Applied Mathematics, 8(5) (2012), 55-71.
  • Cao, J. D., A generalization of the Bernstein Polynomials, J. Math. Analy. and Appl.Math., 122(2000) (1997), 1-21.
  • Lorentz, G. G., Bernstein polynomials, Chelsea, New York, (1986).
  • Gurdek, M., Rempulska, L. and Skorupka, M., The Baskakov operators for functions oftwo variables, Collect. Math., 50(3) (1999), 289–302.
  • Kahvecibasi, I., Approximation properties of the Bernstein-Kantorovich operators on theinterval [-1,1], Master of Science Thesis, Graduate School of Natural and Applied SciencesDepartment of Mathematic, Harran University, Sanlıurfa, Turkey.
  • Volkov, V. I., On the convergence of sequences of linear positive operators in the space oftwo variables, Dokl. Akad. Nauk. SSSR (N.S.), 115 (1957), 17-19.
  • Dirik, F. and Demirci, K., Korovkin type approximation theorem for functions of twovariables in statistical sense, Turk. J. Math., 34 (2010), 73–83.
  • Stancu, D. D., A method for obtaining polynomials of Bernstein type of two variables,Amer. Math. Monthly, 70(3) (1963), 260-264.
  • Gazanfer, A. K. and Büyükyazici, I., Approximation by certain linear positive operatorsof two variables, Hindawi Publishing Corporation Abstract and Applied Analysis, ID 782080,(2014).
  • Sahai, A., An iterative reduced-bias algorithm for a dual-fusion variant of Bernstein’soperator, Inter. Journal of Math. Arch., 2(3) (2011), 331-334.