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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| Language: | English |
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Hindawi Limited
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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doaj-0f80fb9e0ca2418bbc83d8bf80c9edbb2020-11-24T23:24:50ZengHindawi LimitedJournal 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Józef Banaś Rafał Nalepa |
| 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 |
| author_facet |
Józef Banaś Rafał Nalepa |
| author_sort |
Józef Banaś |
| title |
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_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_sort |
on the space of functions with growths tempered by a modulus of continuity and its applications |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 1758-4965 |
| publishDate |
2013-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2013/820437 |
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AT jozefbanas onthespaceoffunctionswithgrowthstemperedbyamodulusofcontinuityanditsapplications AT rafałnalepa onthespaceoffunctionswithgrowthstemperedbyamodulusofcontinuityanditsapplications |
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