Better approximation by Stancu Beta operators in compact interval

Authors

  • Vijay Gupta Netaji Subhas Institute of Technology, India
  • Rani Yadav Netaji Subhas Institute of Technology, India

DOI:

https://doi.org/10.33993/jnaat402-1044

Keywords:

positive linear operators, Korovkin-type approximation theorem, Stancu-Beta operators
Abstract views: 210

Abstract

The present paper deals with the study of Stancu-Beta operators which preserve the constant as well as linear functions but not the quadratic ones. We apply the King's approach to propose the modified form of these operators, so as they preserve the quadratic functions, which results in better approximation for the modified operators in the compact interval \((0,1)\) for these operators.

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References

U. Abel and V. Gupta, Rate of convergence of Stancu Beta operators for functions of bounded variation, Rev. Anal. Number. Théor. Approx., 33 (1), pp. 3-9, 2004, http://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art1

R. A. Devore and G. G. Lorentz, Costructive approximation, Springer, Berlin, 1993. DOI: https://doi.org/10.1007/978-3-662-02888-9

J. P. King, Positive linear operators which preserve x², Acta Math. Hungar., 99(3), pp. 203-208, 2003, https://doi.org/10.1023/a:1024571126455 DOI: https://doi.org/10.1023/A:1024571126455

G. Kirov, and L. Popova, A generalization of the linear positive operators, Mathematica Balkanica, N.S., 7(2), pp. 149-162, 1993.

D. D. Stancu, On the beta approximating oprators of second kind, Rev. Anal. Num. Théor. Approx., 2(4), pp. 231-239, 1995, http://ictp.acad.ro/jnaat/journal/article/view/1995-vol24-nos1-2-art26

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Published

2011-08-01

How to Cite

Gupta, V., & Yadav, R. (2011). Better approximation by Stancu Beta operators in compact interval. Rev. Anal. Numér. Théor. Approx., 40(2), 149–155. https://doi.org/10.33993/jnaat402-1044

Issue

Vol. 40 No. 2 (2011)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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