On the concept of generalized solution of operator equations in banach spaces
We introduce a new concept of generalized solution of operator equations with closed linear operator in a Banach space as an element of the completion of the space in certain locally convex topology. We prove a theorem on the existence and uniqueness of a generalized solution and give examples of fi...
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5242 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511456984825856 |
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| author | Petunin, Yu. I. Петунин, Ю. И. Петунин, Ю. И. |
| author_facet | Petunin, Yu. I. Петунин, Ю. И. Петунин, Ю. И. |
| author_sort | Petunin, Yu. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:28:19Z |
| description | We introduce a new concept of generalized solution of operator equations with closed linear operator in a Banach space as an element of the completion of the space in certain locally convex topology. We prove a theorem on the existence and uniqueness of a generalized solution and give examples of finding the generalized solution for infinite systems of the linear algebraic equations. |
| first_indexed | 2026-03-24T03:13:11Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5242 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:13:11Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/51/1111cb4405db95c0a5de727b449d7551.pdf |
| spelling | umjimathkievua-article-52422020-03-18T21:28:19Z On the concept of generalized solution of operator equations in banach spaces Об одной концепции обобщенного решения операторных уравнений в банаховом пространстве Petunin, Yu. I. Петунин, Ю. И. Петунин, Ю. И. We introduce a new concept of generalized solution of operator equations with closed linear operator in a Banach space as an element of the completion of the space in certain locally convex topology. We prove a theorem on the existence and uniqueness of a generalized solution and give examples of finding the generalized solution for infinite systems of the linear algebraic equations. Визначається поняття узагальненого розв'язку операторного рівняння з замкненим лінійним оператором у банаховому простору'як елемент доповнення простору в деякій локально-опуклій топології. Доведено теорему існування та єдииості узагальненого розв'язку. Розглядаються приклади знаходження узагальненого розв'язку для нескінченних систем лінійних алгебраїчних рівнянь. Institute of Mathematics, NAS of Ukraine 1996-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5242 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 9 (1996); 1286–1290 Український математичний журнал; Том 48 № 9 (1996); 1286–1290 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5242/7177 https://umj.imath.kiev.ua/index.php/umj/article/view/5242/7178 Copyright (c) 1996 Petunin Yu. I. |
| spellingShingle | Petunin, Yu. I. Петунин, Ю. И. Петунин, Ю. И. On the concept of generalized solution of operator equations in banach spaces |
| title | On the concept of generalized solution of operator equations in banach spaces |
| title_alt | Об одной концепции обобщенного решения операторных уравнений
в банаховом пространстве |
| title_full | On the concept of generalized solution of operator equations in banach spaces |
| title_fullStr | On the concept of generalized solution of operator equations in banach spaces |
| title_full_unstemmed | On the concept of generalized solution of operator equations in banach spaces |
| title_short | On the concept of generalized solution of operator equations in banach spaces |
| title_sort | on the concept of generalized solution of operator equations in banach spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5242 |
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