Approximation properties of modified Stancu beta operators
DOI:
https://doi.org/10.33993/jnaat352-845Keywords:
beta operator, degree of approximation, Voronovskaya theoremAbstract
In this paper we give approximation theorems for modified Stancu beta operators of differentiable functions. The Stancu beta operators were examined in [8, 1, 2, 5] and other papers.Downloads
References
Abel, U., Asymptotic approximation with Stancu beta operators, Rev. Anal. Numér. Théor. Approx., 27, no. 1, pp. 5-13, 1998, http://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no1-art2
Abel, U. and Gupta, V., Rate of convergence for Stancu beta operators for functions of bounded variation, Rev. Anal. Numér. Théor. Approx., 33, no. 1, pp. 3-9, 2004, http://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art1
Becker, M., Global approximation theorems for Szász-Mirakyan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J., 27, no. 1, pp. 127-142, 1978.
Fichtenholz, G. M., Calculus, vol. 2, Warsaw 1964.
Gupta, V., Abel, U. and Ivan, M., Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation, Inter. Jour. of Math. and Math. Sciences (in print), https://doi.org/10.1155/ijmms.2005.3827 DOI: https://doi.org/10.1155/IJMMS.2005.3827
Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balkanica, 2, no. 2, pp. 147-153, 1992.
Rempulska, L. and Walczak, Z., Modified Szász-Mirakyan operators, Math. Balkanica, 18, pp. 53-63, 2004.
Stancu, D. D., On the beta approximating operators of second kind, Rev. Anal. Numer. Theor. Approx., 24, nos. 1-2, pp. 231-239, 1995, http://ictp.acad.ro/jnaat/journal/article/view/1995-vol24-nos1-2-art26
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.