Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations
In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/16/1/107 |
| _version_ | 1797342494758797312 |
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| author | Józef Banaś Justyna Madej |
| author_facet | Józef Banaś Justyna Madej |
| author_sort | Józef Banaś |
| collection | DOAJ |
| description | In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper. |
| first_indexed | 2024-03-08T10:34:10Z |
| format | Article |
| id | doaj.art-2ca026632484447cb4c9662a6a439300 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T10:34:10Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2ca026632484447cb4c9662a6a4393002024-01-26T18:38:56ZengMDPI AGSymmetry2073-89942024-01-0116110710.3390/sym16010107Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral EquationsJózef Banaś0Justyna Madej1Department of Nonlinear Analysis, Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, Al. Powstańców Warszawy 8, 35-959 Rzeszów, PolandDepartment of Nonlinear Analysis, Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, Al. Powstańców Warszawy 8, 35-959 Rzeszów, PolandIn this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper.https://www.mdpi.com/2073-8994/16/1/107space of continuous and bounded functionsMNCfixed point theoremIS of IEsasymptotic stability |
| spellingShingle | Józef Banaś Justyna Madej Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations Symmetry space of continuous and bounded functions MNC fixed point theorem IS of IEs asymptotic stability |
| title | Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations |
| title_full | Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations |
| title_fullStr | Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations |
| title_full_unstemmed | Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations |
| title_short | Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations |
| title_sort | asymptotically stable solutions of infinite systems of quadratic hammerstein integral equations |
| topic | space of continuous and bounded functions MNC fixed point theorem IS of IEs asymptotic stability |
| url | https://www.mdpi.com/2073-8994/16/1/107 |
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