TY - JOUR T1 - Approximation properties of Bernstein-Kantorovich type operators of two variables AU - Karahan, Döne AU - İzgi, Aydın PY - 2019 DA - August Y2 - 2019 DO - 10.31801/cfsuasmas.558169 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 2313 EP - 2323 VL - 68 IS - 2 LA - en AB - In this study, the generalized Bernstein-Kantorovich type operatorsare introduced and some approximation properties of these operatorsare studied in the space of continuous functions of two variables ona compact set . The convergence rate of these operators are obtained bymeans of the modulus of continuity. The Voronovskaya type theorem isgiven and some differential properties of these operators are proved. KW - Bernstein-Kantorovich operators KW - modulus of continuity KW - Voronovskaya type theorem CR - 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. CR - Korovkin, P. P., On convergence of linear positive operators in the space of continuousfunctions, Dokl. Akad. Nauk, 90(1953), 961-964. CR - 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. CR - 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). CR - 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. CR - Cao, J. D., A generalization of the Bernstein Polynomials, J. Math. Analy. and Appl.Math., 122(2000) (1997), 1-21. CR - Lorentz, G. G., Bernstein polynomials, Chelsea, New York, (1986). CR - Gurdek, M., Rempulska, L. and Skorupka, M., The Baskakov operators for functions oftwo variables, Collect. Math., 50(3) (1999), 289–302. CR - 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. CR - 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. CR - Dirik, F. and Demirci, K., Korovkin type approximation theorem for functions of twovariables in statistical sense, Turk. J. Math., 34 (2010), 73–83. CR - Stancu, D. D., A method for obtaining polynomials of Bernstein type of two variables,Amer. Math. Monthly, 70(3) (1963), 260-264. CR - Gazanfer, A. K. and Büyükyazici, I., Approximation by certain linear positive operatorsof two variables, Hindawi Publishing Corporation Abstract and Applied Analysis, ID 782080,(2014). CR - 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. UR - https://doi.org/10.31801/cfsuasmas.558169 L1 - https://dergipark.org.tr/en/download/article-file/776410 ER -