AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN'S OPERATORS OF TWO VARIABLES

AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN'S OPERATORS OF TWO VARIABLES

The purpose of this work is to introduce a new class of doublepositive linear operators which depend on a parameter β. For these operators we proved a Korovkin type theorem and we presented some associatedconvergence properties

___

  • Agratini, O., On a sequence of linear and positive operators, Facta Universitatis (Niˇs), Ser. Mat. Inform., 14 (1999), 41-48.
  • Bernstein, S. N. , D´emonstration du th´eor`eme de Weierstrass fond´ee sur le calcul de proba- bilit´es, Comm. Kharkov math. Soc., 13 (1912), 1-2.
  • Consul, P. C., and Jain, G. C., A generalization of the Poisson distribution, Technometrics, 15 (1973), no. 4, 791-799.
  • Dirik, F., and Demirici, K., Korovkin type approximation theorem for functions of two vari- ables in statistical sense, Turk J. Math., 34 (2010), 73-83.
  • Ispir, N., Atakut, C¸ ., Approximation by modified Sz`asz-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. (Math. Sci.), 112 (2002), no. 4, 571-578.
  • Jain, G. C., Approximation of functions by a new class of linear operators, Journal of Aus- tralian Math. Society, 13 (1972), no.3, 271-276.
  • Pringsheim, A., Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann., 53 (1900), 289-321. [11] Robinson, G. M., Divergent double sequences and series, Amer. Math. Soc. Transl., 28 (1926), 50-73.
  • Stancu, D. D., A new class of uniform approximating polynomial operators in two and several variables, Proceedings of the Conference on the Constructive Theory of Functions (Approxi- mation Theory) (Budapest, 1969) pp. (Budapest: Akad´emiai Kiad´o) (1972), 443455.
  • Sz´asz, O., Generalization of S. Bernsteins polynomials to the infinite interval, J. of Research of the Nat. Bur. of Standards, 45 (1950), 239-245.
  • Walczak, Z., Approximation of functions of two variables by some linear positive operators, Acta. Math. Univ. Comenianae, LXXIV (2005), no. 1, 3748.
  • Faculty of Mathematics and Computer Science Babe¸s-Bolyai University Kog˘alniceanu street No. 1, 400084, Cluj-Napoca, Romania
  • E-mail address: anca.farcas@ubbcluj.ro