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Some inequalities of trigonometric approximation in weighted Orlicz spaces

  • Ramazan Akgün EMAIL logo
Published/Copyright: April 29, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

In the present work, we proved a refined direct theorem and an exact inverse theorem of trigonometric approximation in Orlicz spaces with weights satisfying some Muckenhoupt’s Ap condition. As a consequence, refined Marchaud inequality and its inverse are obtained.

Keywords: weighted fractional modulus of smoothness; direct theorem; inverse theorem; fractional derivative; Orlicz space; trigonometric polynomial approximation
MSC: Primary 41A10; 42A10; Secondary 26A33; 41A17; 41A25; 41A27

This work was partially supported by TüB\.ITAK, The Scientific and Technological Research Council of Turkey, 2219 Grant, No. 2012-1-9246 and by MTM2011-27637 and by Balikesir University Scientific Research Project 1.2015.0015.

  1. This paper has been communicated by Ján Borsík

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Received: 2012-9-29
Accepted: 2013-6-4
Published Online: 2016-4-29
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0130
Keywords for this article
weighted fractional modulus of smoothness; direct theorem; inverse theorem; fractional derivative; Orlicz space; trigonometric polynomial approximation

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  11. Research Article
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  13. Research Article
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