On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications
We are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point t...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/820437 |
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| _version_ | 1832562513124786176 |
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| author | Józef Banaś Rafał Nalepa |
| author_facet | Józef Banaś Rafał Nalepa |
| author_sort | Józef Banaś |
| collection | DOAJ |
| description | We are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point theorem, we show the existence theorem for some quadratic integral equations of Fredholm type in the space of functions satisfying the Hölder condition. An example illustrating the mentioned existence result is also included. |
| format | Article |
| id | doaj-art-0f80fb9e0ca2418bbc83d8bf80c9edbb |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-0f80fb9e0ca2418bbc83d8bf80c9edbb2025-02-03T01:22:24ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/820437820437On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its ApplicationsJózef Banaś0Rafał Nalepa1Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 8, 35-959 Rzeszów, PolandDepartment of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 8, 35-959 Rzeszów, PolandWe are going to study the space of real functions defined on a bounded metric space and having growths tempered by a modulus of continuity. We prove also a sufficient condition for the relative compactness in the mentioned function space. Using that condition and the classical Schauder fixed point theorem, we show the existence theorem for some quadratic integral equations of Fredholm type in the space of functions satisfying the Hölder condition. An example illustrating the mentioned existence result is also included.http://dx.doi.org/10.1155/2013/820437 |
| spellingShingle | Józef Banaś Rafał Nalepa On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications Journal of Function Spaces and Applications |
| title | On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications |
| title_full | On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications |
| title_fullStr | On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications |
| title_full_unstemmed | On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications |
| title_short | On the Space of Functions with Growths Tempered by a Modulus of Continuity and Its Applications |
| title_sort | on the space of functions with growths tempered by a modulus of continuity and its applications |
| url | http://dx.doi.org/10.1155/2013/820437 |
| work_keys_str_mv | AT jozefbanas onthespaceoffunctionswithgrowthstemperedbyamodulusofcontinuityanditsapplications AT rafałnalepa onthespaceoffunctionswithgrowthstemperedbyamodulusofcontinuityanditsapplications |