Asymptotic equivalence of sequences and summability
For a sequence-to-sequence transformation A, let RmAx=∑n≥m|(Ax)n| and μmAx=supn≥m|(Ax)n|. The purpose of this paper is to study the relationship between the asymptotic equivalence of two sequences (limnxn/yn=1) and the variations of asymptotic equivalence based on the ratios RmAx/RmAy and μmAx/μmAy....
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297001038 |
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| _version_ | 1832556079990439936 |
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| author | Jinlu Li |
| author_facet | Jinlu Li |
| author_sort | Jinlu Li |
| collection | DOAJ |
| description | For a sequence-to-sequence transformation A, let RmAx=∑n≥m|(Ax)n| and μmAx=supn≥m|(Ax)n|. The purpose of this paper is to study the relationship between the
asymptotic equivalence of two sequences (limnxn/yn=1) and the variations of asymptotic
equivalence based on the ratios RmAx/RmAy and μmAx/μmAy. |
| format | Article |
| id | doaj-art-9e60ab03fb63480f83386e384b223156 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9e60ab03fb63480f83386e384b2231562025-02-03T05:46:32ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120474975710.1155/S0161171297001038Asymptotic equivalence of sequences and summabilityJinlu Li0Department of Mathematics, Shawnee State University, Portsmouth 45662, OH, USAFor a sequence-to-sequence transformation A, let RmAx=∑n≥m|(Ax)n| and μmAx=supn≥m|(Ax)n|. The purpose of this paper is to study the relationship between the asymptotic equivalence of two sequences (limnxn/yn=1) and the variations of asymptotic equivalence based on the ratios RmAx/RmAy and μmAx/μmAy.http://dx.doi.org/10.1155/S0161171297001038asymptotically regularasymptotic equivalence. |
| spellingShingle | Jinlu Li Asymptotic equivalence of sequences and summability International Journal of Mathematics and Mathematical Sciences asymptotically regular asymptotic equivalence. |
| title | Asymptotic equivalence of sequences and summability |
| title_full | Asymptotic equivalence of sequences and summability |
| title_fullStr | Asymptotic equivalence of sequences and summability |
| title_full_unstemmed | Asymptotic equivalence of sequences and summability |
| title_short | Asymptotic equivalence of sequences and summability |
| title_sort | asymptotic equivalence of sequences and summability |
| topic | asymptotically regular asymptotic equivalence. |
| url | http://dx.doi.org/10.1155/S0161171297001038 |
| work_keys_str_mv | AT jinluli asymptoticequivalenceofsequencesandsummability |