Tauberian Theorems for Sequences in 2-Normed Spaces
In this paper we initiate the study of Tauberian theorems for sequences in 2-normed spaces. We introduce a necessary and sufficient Tauberian condition for ( C , 1) summable sequences in such spaces. Corollaries allow this condition to be replaced by 2-normed analogues of Schmidt-type slow oscillati...
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| Veröffentlicht in: | Resultate der Mathematik 2017-12, Vol.72 (4), p.1919-1931 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper we initiate the study of Tauberian theorems for sequences in 2-normed spaces. We introduce a necessary and sufficient Tauberian condition for (
C
, 1) summable sequences in such spaces. Corollaries allow this condition to be replaced by 2-normed analogues of Schmidt-type slow oscillation condition or Hardy-type two-sided condition. |
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| ISSN: | 1422-6383 1420-9012 |
| DOI: | 10.1007/s00025-017-0747-8 |