ON STRONGLY CONDENSING OPERATORS AT INFINITY
The paper introduces the notion of an operator strongly condensing at infinity, which is a natural variation of the notion of a locally strongly condensing operator at a finite point (introduced by the author earlier). It turns out that if such an operator is asymptotically linear, then its asymptot...
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| Format: | Article |
| Language: | Russian |
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Moscow State Technical University of Civil Aviation
2016-11-01
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| Series: | Научный вестник МГТУ ГА |
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| Online Access: | https://avia.mstuca.ru/jour/article/view/240 |
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| _version_ | 1849408712987377664 |
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| author | N. A. Erzakova |
| author_facet | N. A. Erzakova |
| author_sort | N. A. Erzakova |
| collection | DOAJ |
| description | The paper introduces the notion of an operator strongly condensing at infinity, which is a natural variation of the notion of a locally strongly condensing operator at a finite point (introduced by the author earlier). It turns out that if such an operator is asymptotically linear, then its asymptotic derivative is compact. In particular, this notion allows to build examples of operators that are neither compact, nor condensing, not even -bounded. Such operators form a linear space. Some applications of the notion to the theory of bifurcation points are discussed. |
| format | Article |
| id | doaj-art-95e6abb0acfe4f12906c223e542f267d |
| institution | Kabale University |
| issn | 2079-0619 2542-0119 |
| language | Russian |
| publishDate | 2016-11-01 |
| publisher | Moscow State Technical University of Civil Aviation |
| record_format | Article |
| series | Научный вестник МГТУ ГА |
| spelling | doaj-art-95e6abb0acfe4f12906c223e542f267d2025-08-20T03:35:43ZrusMoscow State Technical University of Civil AviationНаучный вестник МГТУ ГА2079-06192542-01192016-11-010207110117240ON STRONGLY CONDENSING OPERATORS AT INFINITYN. A. Erzakova0МГТУ ГАThe paper introduces the notion of an operator strongly condensing at infinity, which is a natural variation of the notion of a locally strongly condensing operator at a finite point (introduced by the author earlier). It turns out that if such an operator is asymptotically linear, then its asymptotic derivative is compact. In particular, this notion allows to build examples of operators that are neither compact, nor condensing, not even -bounded. Such operators form a linear space. Some applications of the notion to the theory of bifurcation points are discussed.https://avia.mstuca.ru/jour/article/view/240measure of noncompactnesscondensing operatorlocally strongly condensing operatorasymptotically linear operatorasymptotic derivativebifurcation point |
| spellingShingle | N. A. Erzakova ON STRONGLY CONDENSING OPERATORS AT INFINITY Научный вестник МГТУ ГА measure of noncompactness condensing operator locally strongly condensing operator asymptotically linear operator asymptotic derivative bifurcation point |
| title | ON STRONGLY CONDENSING OPERATORS AT INFINITY |
| title_full | ON STRONGLY CONDENSING OPERATORS AT INFINITY |
| title_fullStr | ON STRONGLY CONDENSING OPERATORS AT INFINITY |
| title_full_unstemmed | ON STRONGLY CONDENSING OPERATORS AT INFINITY |
| title_short | ON STRONGLY CONDENSING OPERATORS AT INFINITY |
| title_sort | on strongly condensing operators at infinity |
| topic | measure of noncompactness condensing operator locally strongly condensing operator asymptotically linear operator asymptotic derivative bifurcation point |
| url | https://avia.mstuca.ru/jour/article/view/240 |
| work_keys_str_mv | AT naerzakova onstronglycondensingoperatorsatinfinity |