Geodesic
Direct and Inverse Theorems on the Approximation of Functions by Fourier--Laplace Sums in the Spaces $S^{(p,q)}(\sigma^{m-1})$
Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 530-543

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In this paper, we prove direct and inverse theorems on the approximation of functions by Fourier–Laplace sums in the spaces $S^{(p,q)}(\sigma^{m-1})$, $m\ge 3$, in terms of best approximations and moduli of continuity and consider the constructive characteristics of function classes defined by the moduli of continuity of their elements. The given statements generalize the results of the author's work carried out in 2007.
Keywords: approximation of functions, the spaces $S^{(p,q)}(\sigma^{m-1})$, modulus of continuity, Parseval's equality, Jackson-type inequality, Bernstein–Stechkin–Timan-type inequality.
Mots-clés : Fourier–Laplace sum, Gegenbauer polynomial 
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     author = {R. A. Lasuriya},
     title = {Direct and {Inverse} {Theorems} on the {Approximation} of {Functions} by {Fourier--Laplace} {Sums} in the {Spaces} $S^{(p,q)}(\sigma^{m-1})$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {530--543},
     publisher = {mathdoc},
     volume = {98},
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R. A. Lasuriya. Direct and Inverse Theorems on the Approximation of Functions by Fourier--Laplace Sums in the Spaces $S^{(p,q)}(\sigma^{m-1})$. Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 530-543. http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a3/