On calculation of the relative index of a fixed point in the nondegenerate case
The paper is devoted to the calculation of the index of a zero and the asymptotic index of a linear completely continuous nonnegative operator. Also the case of a nonlinear completely continuous operator A whose domain and image are situated in a closed convex set Q of a Banach space is considered....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/86173 |
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| _version_ | 1832551372111740928 |
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| author | A. V. Guminskaya P. P. Zabreiko |
| author_facet | A. V. Guminskaya P. P. Zabreiko |
| author_sort | A. V. Guminskaya |
| collection | DOAJ |
| description | The paper is devoted to the calculation of the index of a zero and
the asymptotic index of a linear completely continuous nonnegative
operator. Also the case of a nonlinear completely continuous
operator A whose domain and image are situated in a closed convex
set Q of a Banach space is considered. For this case, we
formulate the rules for calculating the index of an arbitrary
fixed point and the asymptotic index under the assumption that the
corresponding linearizations exist and the operators of derivative
do not have eigenvectors with eigenvalue 1 in some wedges. |
| format | Article |
| id | doaj-art-0edf811c028445969a09b47abbaf60ed |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0edf811c028445969a09b47abbaf60ed2025-02-03T06:01:31ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/8617386173On calculation of the relative index of a fixed point in the nondegenerate caseA. V. Guminskaya0P. P. Zabreiko1Mechanics and Mathematics Faculty, Belarusian State University, Independence Avenue 4, Minsk 220050, BelarusMechanics and Mathematics Faculty, Belarusian State University, Independence Avenue 4, Minsk 220050, BelarusThe paper is devoted to the calculation of the index of a zero and the asymptotic index of a linear completely continuous nonnegative operator. Also the case of a nonlinear completely continuous operator A whose domain and image are situated in a closed convex set Q of a Banach space is considered. For this case, we formulate the rules for calculating the index of an arbitrary fixed point and the asymptotic index under the assumption that the corresponding linearizations exist and the operators of derivative do not have eigenvectors with eigenvalue 1 in some wedges.http://dx.doi.org/10.1155/AAA/2006/86173 |
| spellingShingle | A. V. Guminskaya P. P. Zabreiko On calculation of the relative index of a fixed point in the nondegenerate case Abstract and Applied Analysis |
| title | On calculation of the relative index of a fixed point in the nondegenerate case |
| title_full | On calculation of the relative index of a fixed point in the nondegenerate case |
| title_fullStr | On calculation of the relative index of a fixed point in the nondegenerate case |
| title_full_unstemmed | On calculation of the relative index of a fixed point in the nondegenerate case |
| title_short | On calculation of the relative index of a fixed point in the nondegenerate case |
| title_sort | on calculation of the relative index of a fixed point in the nondegenerate case |
| url | http://dx.doi.org/10.1155/AAA/2006/86173 |
| work_keys_str_mv | AT avguminskaya oncalculationoftherelativeindexofafixedpointinthenondegeneratecase AT ppzabreiko oncalculationoftherelativeindexofafixedpointinthenondegeneratecase |