Abstract
In this paper, we introduce Stancu type generalization of Dunkl analogue of Szàsz operators. We obtain some direct results, which include asymptotic formula and error estimation in terms of of the modulus continuity. Also, we investigate the convergence of these operators in a weighted space and estimate the rate of convergence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Acar T., Gupta V., Aral A.: Rate of convergence for generalized Szàsz operators. Bull. Math. Sci. 1(1), 99–113 (2011)
Altomare, F., Campiti, M.: Korovkin type approximation theory and its applications. In: De Gruyter Studies in Mathematics, vol. 17. Walter de Gruyter, Berlin, New York (1994)
Aral A., Inoan D., Raşa I.: On the generalized Szàsz–Mirakyan operators. Results Math. 65(3–4), 441–452 (2014)
Ashieser, N.I.: Lecture on Approximation Theory, OGIZ, Moscow-Leningrand, 1947, (in Russian), Theory of approximation (in English). Translated by Hymann, C.J. Frederick Ungar Publishing Co., New York (1956)
Atakut C., Büyükyazıcı İ.: Stancu type generalization of the Favard–Szàsz operators. Appl. Math. Lett. 23, 1479–1482 (2010)
Atakut C., Ispir V.: Approximation by modified Szasz-Mirakjan operators on weighted spaces. Proc. Indian Acad. Sci. Math. 112, 571–578 (2002)
Gadzhiev A.D.: The convergence problem for a sequence of positive linear operators on unbounded sets and theorems analogous to that of P. P. Korovkin. Sov. Math. Dokl. 15(5), 1433–1436 (1974)
Gupta V., Noor M.A., Beniwal M.S.: Rate of convergence in simultaneous approximation for Szàsz-Mirakyan-Durrmeyer operators. J. Math. Anal. Appl. 322(2), 964–970 (2006)
Ispir N.: On modified Baskakov operators on weighted spaces. Turk. J. Math. 26(3), 355–365 (2001)
Karaisa, A.: Approximation by Durrmeyer type Jakimoski–Leviatan operators. Math. Methods Appl. Sci. (2015). doi:10.1002/mma.3650
Karaisa A., Tollu D.T., Asar Y.: Stancu type generalization of q-Favard–Szàsz operators. Appl. Math. Comput. 264, 249–257 (2015)
Lorentz G.G.: Bernstein Polynomials. University of Toronto Press, Toronto (1953)
Stancu D.D.: Approximation of functions by a new class of linear polynomial operators. Rev. Roum. Math. Pure Appl. 13, 1173–1194 (1968)
Sucu S.: Dunkl analogue of Szàsz operators. Appl. Math. Comput. 244, 42–48 (2014)
Szàsz O.: Generalization of S. Bernstein polynomials to the infinite interval. J. Res. Natl. Bur. Stand. 45, 239–245 (1950)
Wood B.: Generalized Szàsz operators for approximation in the complex domain. SIAM J. Appl. Math. 17(4), 790–801 (1969)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Karaisa, A., Karakoç, F. Stancu Type Generalization of Dunkl Analogue of Szàsz Operators. Adv. Appl. Clifford Algebras 26, 1235–1248 (2016). https://doi.org/10.1007/s00006-016-0643-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00006-016-0643-4