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

https://izlik.org/JA32KY36SH

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

https://izlik.org/JA32KY36SH

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
IZ	https://izlik.org/JA32KY36SH
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. https://izlik.org/JA32KY36SH
AMA	1.Farcas A. AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES. Math. Sci. Appl. E-Notes. 2013;1(2):158-164. https://izlik.org/JA32KY36SH
Chicago	Farcas, Anca. 2013. “AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES”. Mathematical Sciences and Applications E-Notes 1 (2): 158-64. https://izlik.org/JA32KY36SH.
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	[1]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, Dec. 2013, [Online]. Available: https://izlik.org/JA32KY36SH
ISNAD	Farcas, Anca. “AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES”. Mathematical Sciences and Applications E-Notes 1/2 (December 1, 2013): 158-164. https://izlik.org/JA32KY36SH.
JAMA	1.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, Dec. 2013, pp. 158-64, https://izlik.org/JA32KY36SH.
Vancouver	1.Anca Farcas. AN APPROXIMATION PROPERTY OF THE GENERALIZED JAIN’S OPERATORS OF TWO VARIABLES. Math. Sci. Appl. E-Notes [Internet]. 2013 Dec. 1;1(2):158-64. Available from: https://izlik.org/JA32KY36SH