Convergence near a point and the Arzela-Ascoli-type theorems
Theorems are proved giving necessary and sufficient conditions for the convergence of a sequence of continuous (differentiable) functions to a continuous (differentiable) function. The concepts of convergence near a point and equipotential convergence near a point are introduced. These concepts are...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5904 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512123900133376 |
|---|---|
| author | Kuzmich, V. I. Кузьмич, В. И. Кузьмич, В. И. |
| author_facet | Kuzmich, V. I. Кузьмич, В. И. Кузьмич, В. И. |
| author_sort | Kuzmich, V. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:20:26Z |
| description | Theorems are proved giving necessary and sufficient conditions for the convergence of a sequence of continuous (differentiable) functions to a continuous (differentiable) function. The concepts of convergence near a point and equipotential convergence near a point are introduced. These concepts are introduced locally; on a segment, they are equivalent to the quasiuniform convergence and to the uniform convergence of a sequence of functions, respectively. |
| first_indexed | 2026-03-24T03:23:47Z |
| format | Article |
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| id | umjimathkievua-article-5904 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:47Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/80/3814a139d14ee6490c13653299aa5780.pdf |
| spelling | umjimathkievua-article-59042020-03-19T09:20:26Z Convergence near a point and the Arzela-Ascoli-type theorems Сходимость возле точки и теоремы типа Арцела - Асколи Kuzmich, V. I. Кузьмич, В. И. Кузьмич, В. И. Theorems are proved giving necessary and sufficient conditions for the convergence of a sequence of continuous (differentiable) functions to a continuous (differentiable) function. The concepts of convergence near a point and equipotential convergence near a point are introduced. These concepts are introduced locally; on a segment, they are equivalent to the quasiuniform convergence and to the uniform convergence of a sequence of functions, respectively. Доведені теореми, які визначають необхідні і достатні умови збіжності послідовності неперервних (диференційовних) функцій до неперервної (диференційовної) функції. Вводяться поняття збіжності біля точки та рівностепеневої збіжності біля точки, які мають локальний характер і рівносильні на відрізку відповідно квазірівномірній і рівномірній збіжностям функціональної послідовності. Institute of Mathematics, NAS of Ukraine 1993-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5904 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 8 (1993); 1090–1095 Український математичний журнал; Том 45 № 8 (1993); 1090–1095 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5904/8491 https://umj.imath.kiev.ua/index.php/umj/article/view/5904/8492 Copyright (c) 1993 Kuzmich V. I. |
| spellingShingle | Kuzmich, V. I. Кузьмич, В. И. Кузьмич, В. И. Convergence near a point and the Arzela-Ascoli-type theorems |
| title | Convergence near a point and the Arzela-Ascoli-type theorems |
| title_alt | Сходимость возле точки и теоремы типа Арцела - Асколи |
| title_full | Convergence near a point and the Arzela-Ascoli-type theorems |
| title_fullStr | Convergence near a point and the Arzela-Ascoli-type theorems |
| title_full_unstemmed | Convergence near a point and the Arzela-Ascoli-type theorems |
| title_short | Convergence near a point and the Arzela-Ascoli-type theorems |
| title_sort | convergence near a point and the arzela-ascoli-type theorems |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5904 |
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