We investigate the approximation properties of the trigonometric system in \( L_{2\pi }^{p\left( \cdot \right)} \). We consider the moduli of smoothness of fractional order and obtain direct and inverse approximation theorems together with a constructive characterization of a Lipschitz-type class.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 1, pp. 3–23, January, 2011.
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Akgün, R. Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent. Ukr Math J 63, 1–26 (2011). https://doi.org/10.1007/s11253-011-0485-0
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DOI: https://doi.org/10.1007/s11253-011-0485-0