Rate of approximation for certain Durrmeyer operators

Abstract

In the present note, we study a certain Durrmeyer type integral modification of Bernstein polynomials. We investigate simultaneous approximation and estimate the rate of convergence in simultaneous approximation.

Authors

V. GUPTA
School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi 110075, India

T. SHERVASHIDZE
A. Razmadze Mathematical Institute, Georgian Academy of Science 1, M. Aleksidze St., Tbilisi 0193 Georgia

M. Craciun
Tiberiu Popoviciu Institute of Numerical Analysis (Romanian Academy)

Keywords

Lebesgue integrable functions, Bernstein polynomials, functions of bounded variation.

Lebesgue integrable functions; Bernstein polynomials; functions of bounded variation.

References

[1] O. Agratini, On the rate of convergence of some integral operators for functions of bounded variation. Studia Sci. Math. Hungar. 42(2005), No. 2, 235–252

[2] R. N. Bhattacharya and R. Ranga Rao, Normal approximation and asymptotic expansions. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York–London–Sydney, 1976.

[3] J. L. Durrmeyer, Une formule d’inversion de la transformee de Laplace: Application a la Theorie des Moments. These de 3e cycles, Faculte des Sciences de l’ Universite de Paris, 1967.

[4] S. S. Guo, On the rate of convergence of the Durrmeyer operator for functions of bounded variation. J. Approx. Theory 51(1987), No. 2, 183–192.

[5] V. Gupta, A note on the rate of convergence of Durrmeyer type operators for function of bounded variation. Soochow J. Math. 23(1997), No. 1, 115–118.

[6] V. Gupta and P. Maheshwari, Bezier variant of a new Durrmeyer type operators. Riv. Mat. Univ. Parma (7) 2(2003), 9–21.

[7] V. Gupta and G. S. Srivastava, Approximation by Durrmeyer-type operators. Ann. Polon. Math. 64(1996), No. 2, 153–159.

[8] X. M. Zeng, Bounds for Bernstein basis functions and Meyer–Konig and Zeller basis functions, J. Math. Anal. Appl. 219(1998), No. 2, 364–376.

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About this paper

Journal

Georgian Mathematical Journal

Publisher Name

De Gruyter

DOI

10.1515/GMJ.2006.277

Print ISSN

1072-947X

Online ISSN

Not available yet.

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