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

Anca Farcas

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

Year 2013, Volume: 1 Issue: 2, 158 - 164, 01.12.2013

Abstract

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

Keywords

double sequence of positive linear operators , Korovkin theorem , Astatistical convergence for double sequences , modulus of continuity

References

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

Year 2013, Volume: 1 Issue: 2, 158 - 164, 01.12.2013

Anca Farcas

Abstract

References

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

There are 12 citations in total.

Details

Primary Language	English
Authors	Anca Farcas This is me
Submission Date	March 9, 2015
Publication Date	December 1, 2013
Published in Issue	Year 2013 Volume: 1 Issue: 2

Cite

APA	Farcas, A. (2013). AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES. Mathematical Sciences and Applications E-Notes, 1(2), 158-164.
AMA	Farcas A. AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES. Math. Sci. Appl. E-Notes. December 2013;1(2):158-164.
Chicago	Farcas, Anca. “AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES”. Mathematical Sciences and Applications E-Notes 1, no. 2 (December 2013): 158-64.
EndNote	Farcas A (December 1, 2013) AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES. Mathematical Sciences and Applications E-Notes 1 2 158–164.
IEEE	A. Farcas, “AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES”, Math. Sci. Appl. E-Notes, vol. 1, no. 2, pp. 158–164, 2013.
ISNAD	Farcas, Anca. “AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES”. Mathematical Sciences and Applications E-Notes 1/2 (December2013), 158-164.
JAMA	Farcas A. AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES. Math. Sci. Appl. E-Notes. 2013;1:158–164.
MLA	Farcas, Anca. “AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES”. Mathematical Sciences and Applications E-Notes, vol. 1, no. 2, 2013, pp. 158-64.
Vancouver	Farcas A. AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES. Math. Sci. Appl. E-Notes. 2013;1(2):158-64.