On the Approximation Properties of Cesàro Means of Negative Order for the Double Vilenkin–Fourier Series

We establish approximation properties of Cesàro ( C,−α,−β ) means with α, β ε (0 , 1) for the Vilenkin–Fourier series. This result enables one to establish a condition sufficient for the convergence of the means σ n , m − α , − β ( x, y, f ) to f ( x, y ) in the L p -metric.

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Bibliographische Detailangaben
Veröffentlicht in:	Ukrainian mathematical journal 2020-08, Vol.72 (3), p.446-463
1. Verfasser:	Tepnadze, T.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Approximation Fourier series Geometry Mathematical analysis Mathematics Mathematics and Statistics Statistics
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Beschreibung
Zusammenfassung:	We establish approximation properties of Cesàro ( C,−α,−β ) means with α, β ε (0 , 1) for the Vilenkin–Fourier series. This result enables one to establish a condition sufficient for the convergence of the means σ n , m − α , − β ( x, y, f ) to f ( x, y ) in the L p -metric.
ISSN:	0041-5995 1573-9376
DOI:	10.1007/s11253-020-01792-z