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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 19, Issue 4

Issues

On approximation by trigonometric polynomials in Orlicz spaces

Sadulla Z. Jafarov
  • Department of Mathematics, Faculty of Art and Sciences, Pamukkale University, 20017, Denizli, Turkey; and Mathematics and Mechanics Institute, Azerbaijan National Academy of Sciences, Az-1141, Baku, Azerbaijan
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/ Jamal I. Mamedkhanov
  • Mathematics and Mechanics Institute, Azerbaijan National Academy of Sciences, Az-1141, Baku; and Department of Function Theory and Functional Analysis, Baku State University, Az-1145, Baku, Azerbaijan
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Published Online: 2012-12-01 | DOI: https://doi.org/10.1515/gmj-2012-0043

Abstract.

Let T denote the interval . In this paper, some theorems for approximation by trigonometric polynomials in the Orlicz space are proved. Under certain conditions, we prove the existence of derivatives of functions belonging to the Orlicz space and investigate the approximation properties of the derivatives of trigonometric polynomials. Note that the estimate obtained between the derivatives of functions and the derivatives of trigonometric polynomials depends on a sequence of best approximations in the Orlicz space .

Keywords: Young function; Orlicz space; Boyd indices; modulus of smoothness; best approximation

About the article

Received: 2011-03-22

Revised: 2011-12-06

Published Online: 2012-12-01

Published in Print: 2012-12-01


Citation Information: , Volume 19, Issue 4, Pages 687–695, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0043.

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