Reyhan Canatan Ilbey



Weighted Approximation Properties of Dunkl Analogue of Modified Szász-Mirakjan Operators

pdf PDF


Our goal in this paper is to introduce a modified Szász-Mirakjan operators via Dunkl analogue and investigate their approximation properties by using weighted Korovkin theorem. At the end of this study it is concluded that our modified operator can be compared with Dunkl analogue of Szász operators.


Dunkl operator, Szász-Mirakjan operators, weighted Korovkin theorem, weighted modulus of continuity


[1] Altomare, F., & Campiti, M. , Korovkin-type approximation theory and its applications (Vol. 17). Walter de Gruyter, 1994.

[2] Gadzhiev, A. D., The convergence problem for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of PP Korovkin. In Soviet Math. Dokl. , Vol. 15, No. 5, 1974, pp. 1433-1436.

[3] Gupta, V., & Pant, R. P., Rate of convergence for the modified Szász–Mirakyan operators on functions of bounded variation, Journal of Mathematical Analysis and Applications, 233(2), 1999, 476-483.

[4] Ispir, N., On modified Baskakov operators on weighted spaces, Turkish Journal of Mathematics, 25(3), 2001, 355-365.

[5] Ispir, N., & Atakut, C., Approximation by modified Szasz-Mirakjan operators on weighted spaces. Proc. Indian Acad. Sci.(Math. Sci.), 112(4), 2002, 571-578.

[6] Rosenblum, M., Generalized Hermite polynomials and the Bose-like oscillator calculus, Oper. Theory, Adv. Appl., 73, 1994, 369-396.

[7] Szász, O., Generalization of S. Bernstein’s polynomials to the infinite interval, J. Res. Nat. Bur. Standards, 45, 1950, 239-245.

[8] Sucu, S., Dunkl analogue of Szász operators. Applied Mathematics and Computation, 244, 2014, 42-48.

[9] Walczak, Z., On approximation by modified Szasz-Mirakyan operators. Glasnik matematički, 37(2), 2002, 303-319.

[10] Walczak, Z., On modified Szasz–Mirakyan operators. Novi Sad J. Math, 33(1), 2003, 93-107

Cite this paper

Reyhan Canatan Ilbey. (2017) Weighted Approximation Properties of Dunkl Analogue of Modified Szász-Mirakjan Operators. International Journal of Mathematical and Computational Methods, 2, 341-345


Copyright © 2017 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0