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Absolute Summability Factors in a Sequence
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| Zeitschriftentitel: | Canadian Mathematical Bulletin |
|---|---|
| Personen und Körperschaften: | |
| In: | Canadian Mathematical Bulletin, 27, 1984, 1, S. 16-30 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Canadian Mathematical Society
|
| Schlagwörter: |
| author_facet |
Baron, S. Baron, S. |
|---|---|
| author |
Baron, S. |
| spellingShingle |
Baron, S. Canadian Mathematical Bulletin Absolute Summability Factors in a Sequence General Mathematics |
| author_sort |
baron, s. |
| spelling |
Baron, S. 0008-4395 1496-4287 Canadian Mathematical Society General Mathematics http://dx.doi.org/10.4153/cmb-1984-003-7 <jats:title>Abstract</jats:title><jats:p>Let α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (ε<jats:sub>n</jats:sub>) in order that the sequence (ε<jats:sub>n</jats:sub><jats:italic>U</jats:italic><jats:sub>n</jats:sub>) will be absolutely summable by the Cesàro method C<jats:sup>β</jats:sup> for each sequence (<jats:italic>U<jats:sub>n</jats:sub></jats:italic>) which is bounded or summable by the method C<jats:sup>α</jats:sup></jats:p><jats:p>Another theorem is proven when C<jats:sup>α</jats:sup> and C<jats:sup>β</jats:sup> are replaced by triangular methods A = (a<jats:sub>nk</jats:sub>) and <jats:italic>B</jats:italic>=(<jats:italic>b<jats:sub>nk</jats:sub></jats:italic>) satisfying <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S000843950006611X_inline1" />, where (ξ<jats:sub>nk</jats:sub>) = (ank)<jats:sup>-1</jats:sup>.</jats:p> Absolute Summability Factors in a Sequence Canadian Mathematical Bulletin |
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Canadian Mathematical Society, 1984 |
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Canadian Mathematical Society, 1984 |
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0008-4395 1496-4287 |
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0008-4395 1496-4287 |
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1984 |
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Canadian Mathematical Society |
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Canadian Mathematical Bulletin |
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49 |
| title |
Absolute Summability Factors in a Sequence |
| title_unstemmed |
Absolute Summability Factors in a Sequence |
| title_full |
Absolute Summability Factors in a Sequence |
| title_fullStr |
Absolute Summability Factors in a Sequence |
| title_full_unstemmed |
Absolute Summability Factors in a Sequence |
| title_short |
Absolute Summability Factors in a Sequence |
| title_sort |
absolute summability factors in a sequence |
| topic |
General Mathematics |
| url |
http://dx.doi.org/10.4153/cmb-1984-003-7 |
| publishDate |
1984 |
| physical |
16-30 |
| description |
<jats:title>Abstract</jats:title><jats:p>Let α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (ε<jats:sub>n</jats:sub>) in order that the sequence (ε<jats:sub>n</jats:sub><jats:italic>U</jats:italic><jats:sub>n</jats:sub>) will be absolutely summable by the Cesàro method C<jats:sup>β</jats:sup> for each sequence (<jats:italic>U<jats:sub>n</jats:sub></jats:italic>) which is bounded or summable by the method C<jats:sup>α</jats:sup></jats:p><jats:p>Another theorem is proven when C<jats:sup>α</jats:sup> and C<jats:sup>β</jats:sup> are replaced by triangular methods A = (a<jats:sub>nk</jats:sub>) and <jats:italic>B</jats:italic>=(<jats:italic>b<jats:sub>nk</jats:sub></jats:italic>) satisfying <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S000843950006611X_inline1" />, where (ξ<jats:sub>nk</jats:sub>) = (ank)<jats:sup>-1</jats:sup>.</jats:p> |
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| description | <jats:title>Abstract</jats:title><jats:p>Let α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (ε<jats:sub>n</jats:sub>) in order that the sequence (ε<jats:sub>n</jats:sub><jats:italic>U</jats:italic><jats:sub>n</jats:sub>) will be absolutely summable by the Cesàro method C<jats:sup>β</jats:sup> for each sequence (<jats:italic>U<jats:sub>n</jats:sub></jats:italic>) which is bounded or summable by the method C<jats:sup>α</jats:sup></jats:p><jats:p>Another theorem is proven when C<jats:sup>α</jats:sup> and C<jats:sup>β</jats:sup> are replaced by triangular methods A = (a<jats:sub>nk</jats:sub>) and <jats:italic>B</jats:italic>=(<jats:italic>b<jats:sub>nk</jats:sub></jats:italic>) satisfying <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S000843950006611X_inline1" />, where (ξ<jats:sub>nk</jats:sub>) = (ank)<jats:sup>-1</jats:sup>.</jats:p> |
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| imprint | Canadian Mathematical Society, 1984 |
| imprint_str_mv | Canadian Mathematical Society, 1984 |
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| issn | 0008-4395, 1496-4287 |
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| physical | 16-30 |
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| series | Canadian Mathematical Bulletin |
| source_id | 49 |
| spelling | Baron, S. 0008-4395 1496-4287 Canadian Mathematical Society General Mathematics http://dx.doi.org/10.4153/cmb-1984-003-7 <jats:title>Abstract</jats:title><jats:p>Let α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (ε<jats:sub>n</jats:sub>) in order that the sequence (ε<jats:sub>n</jats:sub><jats:italic>U</jats:italic><jats:sub>n</jats:sub>) will be absolutely summable by the Cesàro method C<jats:sup>β</jats:sup> for each sequence (<jats:italic>U<jats:sub>n</jats:sub></jats:italic>) which is bounded or summable by the method C<jats:sup>α</jats:sup></jats:p><jats:p>Another theorem is proven when C<jats:sup>α</jats:sup> and C<jats:sup>β</jats:sup> are replaced by triangular methods A = (a<jats:sub>nk</jats:sub>) and <jats:italic>B</jats:italic>=(<jats:italic>b<jats:sub>nk</jats:sub></jats:italic>) satisfying <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S000843950006611X_inline1" />, where (ξ<jats:sub>nk</jats:sub>) = (ank)<jats:sup>-1</jats:sup>.</jats:p> Absolute Summability Factors in a Sequence Canadian Mathematical Bulletin |
| spellingShingle | Baron, S., Canadian Mathematical Bulletin, Absolute Summability Factors in a Sequence, General Mathematics |
| title | Absolute Summability Factors in a Sequence |
| title_full | Absolute Summability Factors in a Sequence |
| title_fullStr | Absolute Summability Factors in a Sequence |
| title_full_unstemmed | Absolute Summability Factors in a Sequence |
| title_short | Absolute Summability Factors in a Sequence |
| title_sort | absolute summability factors in a sequence |
| title_unstemmed | Absolute Summability Factors in a Sequence |
| topic | General Mathematics |
| url | http://dx.doi.org/10.4153/cmb-1984-003-7 |