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Georgian Mathematical Journal

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

Editorial Board: 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, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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Volume 23, Issue 4

Issues

Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators

Tuncer Acar
Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/gmj-2016-0007

Abstract

In the present paper, we mainly study quantitative Voronovskaya-type theorems for q-Szász operators defined in [20]. We consider weighted spaces of functions and the corresponding weighted modulus of continuity. We obtain the quantitative q-Voronovskaya-type theorem and the q-Grüss–Voronovskaya-type theorem in terms of the weighted modulus of continuity of q-derivatives of the approximated function. In this way, we either obtain the rate of pointwise convergence of q-Szász operators or we present these results for a subspace of continuous functions, although the classical ones are valid for differentiable functions.

Keywords: Voronovskaya-type theorem

MSC 2010: 41A25; 41A36

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About the article

Received: 2014-09-08

Revised: 2015-01-15

Accepted: 2015-01-30

Published Online: 2016-03-10

Published in Print: 2016-12-01


Citation Information: Georgian Mathematical Journal, Volume 23, Issue 4, Pages 459–468, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2016-0007.

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