Approximation properties of modified Stancu beta operators

Authors

  • L. Rempulska Poznan University of Technology, Poland
  • M. Skorupka Poznan University of Technology, Poland

DOI:

https://doi.org/10.33993/jnaat352-845

Keywords:

beta operator, degree of approximation, Voronovskaya theorem
Abstract views: 219

Abstract

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

Download data is not yet available.

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

2006-08-01

How to Cite

Rempulska, L., & Skorupka, M. (2006). Approximation properties of modified Stancu beta operators. Rev. Anal. Numér. Théor. Approx., 35(2), 189–197. https://doi.org/10.33993/jnaat352-845

Issue

Section

Articles