Asymptotic equivalence and summability
This paper is a study of the relatioship. between the asymptotic equivalence of two sequences (limnxn/yn=1) and three variatious of this equivalence for a sequence-to-sequence transformation A, the three variations are give by the ratios RmAx/RmAy. SmAx/SmAy, And μmAx/μmAy, where RmAz:=∑n≥m|(Az)n|,...
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000948 |
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| _version_ | 1832563095642308608 |
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| author | Mousa S. Marouf |
| author_facet | Mousa S. Marouf |
| author_sort | Mousa S. Marouf |
| collection | DOAJ |
| description | This paper is a study of the relatioship. between the asymptotic equivalence of two
sequences (limnxn/yn=1) and three variatious of this equivalence for a sequence-to-sequence
transformation A, the three variations are give by the ratios RmAx/RmAy. SmAx/SmAy, And μmAx/μmAy, where RmAz:=∑n≥m|(Az)n|, SmAz:=∑n≤m|(Az)n|, and μmAz:=supn≥m|(Az)n|. |
| format | Article |
| id | doaj-art-7b8729aa726a4445852059c375d15ebe |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7b8729aa726a4445852059c375d15ebe2025-02-03T01:20:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116475576210.1155/S0161171293000948Asymptotic equivalence and summabilityMousa S. Marouf0Shawnee State University, 940 2nd Street, Portsmouth 45662, Ohio, USAThis paper is a study of the relatioship. between the asymptotic equivalence of two sequences (limnxn/yn=1) and three variatious of this equivalence for a sequence-to-sequence transformation A, the three variations are give by the ratios RmAx/RmAy. SmAx/SmAy, And μmAx/μmAy, where RmAz:=∑n≥m|(Az)n|, SmAz:=∑n≤m|(Az)n|, and μmAz:=supn≥m|(Az)n|.http://dx.doi.org/10.1155/S0161171293000948asymptotically regularasymptotic equivalenceNörland-type matrix N¯p. |
| spellingShingle | Mousa S. Marouf Asymptotic equivalence and summability International Journal of Mathematics and Mathematical Sciences asymptotically regular asymptotic equivalence Nörland-type matrix N¯p. |
| title | Asymptotic equivalence and summability |
| title_full | Asymptotic equivalence and summability |
| title_fullStr | Asymptotic equivalence and summability |
| title_full_unstemmed | Asymptotic equivalence and summability |
| title_short | Asymptotic equivalence and summability |
| title_sort | asymptotic equivalence and summability |
| topic | asymptotically regular asymptotic equivalence Nörland-type matrix N¯p. |
| url | http://dx.doi.org/10.1155/S0161171293000948 |
| work_keys_str_mv | AT mousasmarouf asymptoticequivalenceandsummability |