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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| Veröffentlicht in: | Ukrainian mathematical journal 2020-08, Vol.72 (3), p.446-463 |
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| container_end_page | 463 |
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| container_issue | 3 |
| container_start_page | 446 |
| container_title | Ukrainian mathematical journal |
| container_volume | 72 |
| creator | Tepnadze, T. |
| description | 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. |
| doi_str_mv | 10.1007/s11253-020-01792-z |
| format | Article |
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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
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L
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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
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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.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11253-020-01792-z</doi><tpages>18</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2020-08, Vol.72 (3), p.446-463 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_proquest_journals_2450308556 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Approximation Fourier series Geometry Mathematical analysis Mathematics Mathematics and Statistics Statistics |
| title | On the Approximation Properties of Cesàro Means of Negative Order for the Double Vilenkin–Fourier Series |
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