Approximation of functions belonging to the weighted L(a, M, omega)-class by trigonometric polynomials

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New Zealand Journal of Mathematics

Vol. 48, (2018), Pages 11-23

Department of Mathematics and Science Education,

Faculty of Education,

Mus Alparslan University,

49250, Mus,

Turkey.

Abstract In this work the approximation of the functions by means $t_{n}(f;x),~N_{n}^{\beta }(f;x)$ and $R_{n}^{\beta }(f,x)$ of the trigonometric Fourier series in weighted Orlicz spaces with Muckenhoupt weights are studied.

Keywords Trigonometric approximation, Orlicz space, weighted Orlicz space, Boyd indices, Muckenhoupt weight, weighted $L(\alpha ,M,\omega )$ class, modulus of continuity.

Classification (MSC2000) 41A17, 41A25, 41A27, 42A10, 42A50, 46E30, 46E35, 26A33.