Trigonometric approximation of functions in seminormed spaces. (English) Zbl 1466.42003
Summary: In this paper, we study the approximation properties of \(2\pi\)-periodic functions in a seminormed space. We use a general matrix method of summability, and the moduli of continuity in the seminormed space as a measure of approximation. Our results generalize and improve some of the previous results available in the literature.
MSC:
| 42A10 | Trigonometric approximation |
| 40C05 | Matrix methods for summability |
| 41A25 | Rate of convergence, degree of approximation |
| 42A24 | Summability and absolute summability of Fourier and trigonometric series |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
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