We prove some new estimates useful in applications to the approximation of some classes of functions characterized by the generalized continuity modulus from the space \({\mathbb{L}}_{2}^{\left(\alpha ,\beta \right)}\) by partial sums of the Jacobi – Dunkl series. For this purpose, we use the generalized Jacobi – Dunkl translation operator obtained by Vinogradov in the monograph [Theory of Approximation of Functions of Real Variable [in Russian], Fizmatgiz, Moscow (1960)].
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 10, pp. 1427–1440, October, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i10.6275.
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Tyr, O., Daher, R. On the Approximation of Functions by Jacobi–Dunkl Expansions in the Weighted Space\({\mathbb{L}}_{2}^{\left(\alpha ,\beta \right)}\). Ukr Math J 74, 1629–1644 (2023). https://doi.org/10.1007/s11253-023-02159-w
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DOI: https://doi.org/10.1007/s11253-023-02159-w