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Modulus of Smoothness and Theorems Concerning Approximation in the Space \(L^{2}_{q,\alpha }(\mathbb {R}_{q})\) with Power Weight

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Abstract

In this work, we look at problems in the theory of approximation of functions on the space \(L_{q,\alpha }^{2}(\mathbb {R}_{q})\) with power weight. We prove analogues of the direct Jackson’s theorems for the modulus of smoothness (of arbitrary order) constructed using the generalized q-Dunkl translation operator. We also show that the modulus of smoothness and the K-functional constructed from the Sobolev-type space corresponding to the q-Dunkl operator are equivalent.

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Acknowledgements

The authors are grateful to the referees for the useful comments and suggestions in improving the presentation of the paper.

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  1. Department of Mathematics, Faculty of Sciences Aïn Chock, University Hassan II, Casablanca, Morocco

    Radouan Daher & Othman Tyr

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  1. Radouan Daher
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  2. Othman Tyr
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Correspondence to Othman Tyr.

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Daher, R., Tyr, O. Modulus of Smoothness and Theorems Concerning Approximation in the Space \(L^{2}_{q,\alpha }(\mathbb {R}_{q})\) with Power Weight. Mediterr. J. Math. 18, 69 (2021). https://doi.org/10.1007/s00009-021-01715-7

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  • DOI: https://doi.org/10.1007/s00009-021-01715-7

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