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Publication Date:
March 2010
ISSN:
1572-9176
DOI:
10.1515/GMJ.2008.591

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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.

Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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On Iterative Combination of Modified Bernstein-Type Polynomials

P. N. Agrawal1 / Asha Ram Gairola2 / Vijay Gupta3

1Department of Mathematics, I.I.T. Roorkee, Roorkee 247667, India. E-mail: pnappfma@iitr.ernet.in

2Department of Mathematics, I.I.T. Roorkee, Roorkee 247667, India. E-mail: ashagairola@yahoo.co.in

3School of Applied Sciences Netaji Subhas, Institute of Technology, Sector 3 Dwarka, New Delhi 110078, India. E-mail: vijay@nsit.ac.in

Citation Information: Georgian Mathematical Journal. Volume 15, Issue 4, Pages 591–600, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2008.591, March 2010

Publication History:
Received:
2006-12-20
Published Online:
2010-03-11

Abstract

The paper deals with some direct results on ordinary and simultaneous approximations for iterative combinations of a new type of Bernstein–Durrmeyer operators. Gupta and Vasishtha [Math. Comput. Modelling 39: 521–527, 2004] have recently claimed that iterative combinations can be applied only for those operators for which 𝑡 maps exactly to 𝑥. Here we disagree with their claim and state that iterative combinations can be applied for other operators which do not reproduce linear functions either.

Key words and phrases:: Bernstein type polynomials; iterative combinations; ordinary approximation; simultaneous approximation

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