On inequalities of the parallelogram in the Banach space and certain properties of dual mapping
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| Datum: | 1988 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch |
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Institute of Mathematics, NAS of Ukraine
1988
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9288 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513471704072192 |
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| author | Alber , Ya. I. Notik , A. I. Альбер , Я. И. Нотик , А. И. |
| author_facet | Alber , Ya. I. Notik , A. I. Альбер , Я. И. Нотик , А. И. |
| author_sort | Alber , Ya. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-06-18T12:19:17Z |
| description | - |
| first_indexed | 2026-03-24T03:45:13Z |
| format | Article |
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| id | umjimathkievua-article-9288 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:45:13Z |
| publishDate | 1988 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/0b/6fccfcf5767031c1e0387993b98c5f0b.pdf |
| spelling | umjimathkievua-article-92882025-06-18T12:19:17Z On inequalities of the parallelogram in the Banach space and certain properties of dual mapping О неравенствах параллелограмма в банаховых пространствах и некоторых свойствах дуального отображения Alber , Ya. I. Notik , A. I. Альбер , Я. И. Нотик , А. И. - В произвольном банаховом пространстве $b$ установлены нижнее и верхнее неравенства параллелограмма: \[2 || x ||^2 + 2 || y ||^2 - || x + y ||^2 \geq L^{-1}\delta_B(|| x-y||/C_1),\] \[C_1 = 2{\rm max}(1, \sqrt{(||x ||^2 + || y||^2)/2)},\] \[2||x||^2+2||y||^2-||x+y||^2\leq 4||x-y||^2 + C_2\rho_B(||x-y||),\] \[C_2 = 4{\rm max} (L, (|| x || + ||y||)/2), \quad 0 <L<3,18,\] где $\delta_B$ и $\rho_B(\tau)$ — соответственно модули выпуклости и гладкости пространства $B$. Вычислены модули непрерывности и монотонности нормализованного дуального отображения. Institute of Mathematics, NAS of Ukraine 1988-11-01 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9288 Ukrains’kyi Matematychnyi Zhurnal; Vol. 40 No. 6 (1988); 769-771 Український математичний журнал; Том 40 № 6 (1988); 769-771 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9288/10463 Copyright (c) 1988 Я. И. Альбер , А. И. Нотик |
| spellingShingle | Alber , Ya. I. Notik , A. I. Альбер , Я. И. Нотик , А. И. On inequalities of the parallelogram in the Banach space and certain properties of dual mapping |
| title | On inequalities of the parallelogram in the Banach space and certain properties of dual mapping |
| title_alt | О неравенствах параллелограмма в банаховых пространствах и некоторых свойствах дуального отображения |
| title_full | On inequalities of the parallelogram in the Banach space and certain properties of dual mapping |
| title_fullStr | On inequalities of the parallelogram in the Banach space and certain properties of dual mapping |
| title_full_unstemmed | On inequalities of the parallelogram in the Banach space and certain properties of dual mapping |
| title_short | On inequalities of the parallelogram in the Banach space and certain properties of dual mapping |
| title_sort | on inequalities of the parallelogram in the banach space and certain properties of dual mapping |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9288 |
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