On  On the approximation of functions by Jacobi – Dunkl expansion in the weighted space $\mathbb{L}_{2}^{(\alpha,\beta)}$

O.  Tyr; R.  Daher

doi:10.37863/umzh.v74i10.6275

O. Tyr Univ. Hassan II, Casablanca, Morocco
R. Daher Univ. Hassan II, Casablanca, Morocco

DOI: https://doi.org/10.37863/umzh.v74i10.6275

Keywords: JACOBI – DUNKL EXPANSION

Abstract

UDC 517.5

We prove some new estimates useful in applications for the approximation of certain classes of functions characterized by the generalized continuity modulus from the space $\mathbb{L}_{2}^{(\alpha,\beta)}$ 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, Fizmatgiz, Moscow (1960) (in Russian)].

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