On necessary and sufficient conditions for the summability of a numerical series to imply its convergence
On the basis of the concepts of (C) -point and (¯R, p)-point of a sequence of complex numbers introduced by the author and results established earlier, we formulate necessary and sufficient conditions for the summability of a number series by a positive Cesaro method or the Riesz method to imply the...
Збережено в:
| Дата: | 1995 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1995
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5467 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511695038840832 |
|---|---|
| author | Davydov, N. A. Давыдов, Н. А. Давыдов, Н. А. |
| author_facet | Davydov, N. A. Давыдов, Н. А. Давыдов, Н. А. |
| author_sort | Davydov, N. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:11:22Z |
| description | On the basis of the concepts of (C) -point and (¯R, p)-point of a sequence of complex numbers introduced by the author and results established earlier, we formulate necessary and sufficient conditions for the summability of a number series by a positive Cesaro method or the Riesz method to imply the convergence of this series. We also present a sufficient condition for summability to imply the convergence of a subsequence of its partial sums. |
| first_indexed | 2026-03-24T03:16:58Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5467 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:16:58Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a3/714473dd5623e5335144c81bdf0188a3.pdf |
| spelling | umjimathkievua-article-54672020-03-19T09:11:22Z On necessary and sufficient conditions for the summability of a numerical series to imply its convergence О необходимых и достаточных условиях, при которых из суммируемости числового ряда следует его сходимость Davydov, N. A. Давыдов, Н. А. Давыдов, Н. А. On the basis of the concepts of (C) -point and (¯R, p)-point of a sequence of complex numbers introduced by the author and results established earlier, we formulate necessary and sufficient conditions for the summability of a number series by a positive Cesaro method or the Riesz method to imply the convergence of this series. We also present a sufficient condition for summability to imply the convergence of a subsequence of its partial sums. ТІа основі введених автором раніше понять $(С)$- і $(R, р)$-точки послідовності комплексних чисел і одержаних ним результатів сформульовані необхідні і достатні умови того, щоб із сумовності числового ряду яким-небудь додатним методом Чезаро або методом Pica випливала збіжність цього ряду, і достатня умова того, щоб із сумовності ряду цими методами випливала збіжність під послідовності його частинних сум. Institute of Mathematics, NAS of Ukraine 1995-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5467 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 6 (1995); 747–754 Український математичний журнал; Том 47 № 6 (1995); 747–754 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5467/7623 https://umj.imath.kiev.ua/index.php/umj/article/view/5467/7624 Copyright (c) 1995 Davydov N. A. |
| spellingShingle | Davydov, N. A. Давыдов, Н. А. Давыдов, Н. А. On necessary and sufficient conditions for the summability of a numerical series to imply its convergence |
| title | On necessary and sufficient conditions for the summability of a numerical series to imply its convergence |
| title_alt | О необходимых и достаточных условиях, при которых из суммируемости
числового ряда следует его сходимость |
| title_full | On necessary and sufficient conditions for the summability of a numerical series to imply its convergence |
| title_fullStr | On necessary and sufficient conditions for the summability of a numerical series to imply its convergence |
| title_full_unstemmed | On necessary and sufficient conditions for the summability of a numerical series to imply its convergence |
| title_short | On necessary and sufficient conditions for the summability of a numerical series to imply its convergence |
| title_sort | on necessary and sufficient conditions for the summability of a numerical series to imply its convergence |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5467 |
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