A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications
We present a novel result that, in a certain sense, generalizes the Arzelà-Ascoli theorem. Our main tool will be the so called degree of nondensifiability, which is not a measure of noncompactness but canbe used as an alternative tool in certain fixed problems where such measures do not wor...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2019-04-01
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| Series: | Applied General Topology |
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| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/10930 |
| _version_ | 1818427554679226368 |
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| author | G. García |
| author_facet | G. García |
| author_sort | G. García |
| collection | DOAJ |
| description | We present a novel result that, in a certain sense, generalizes the Arzelà-Ascoli theorem. Our main tool will be the so called degree of nondensifiability, which is not a measure of noncompactness but canbe used as an alternative tool in certain fixed problems where such measures do not work out. To justify our results, we analyze the existence of continuous solutions of certain Volterra integral equations defined by vector valued functions. |
| first_indexed | 2024-12-14T14:47:35Z |
| format | Article |
| id | doaj.art-bbcd97a8defa471d940dd16abe51ebe3 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-14T14:47:35Z |
| publishDate | 2019-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-bbcd97a8defa471d940dd16abe51ebe32022-12-21T22:57:14ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472019-04-0120126527910.4995/agt.2019.109307399A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applicationsG. García0UNEDWe present a novel result that, in a certain sense, generalizes the Arzelà-Ascoli theorem. Our main tool will be the so called degree of nondensifiability, which is not a measure of noncompactness but canbe used as an alternative tool in certain fixed problems where such measures do not work out. To justify our results, we analyze the existence of continuous solutions of certain Volterra integral equations defined by vector valued functions.https://polipapers.upv.es/index.php/AGT/article/view/10930Arzelà-Ascoli theoremdegree of nondensifiabilityα-dense curvesmeasures of noncompactnessVolterra integral equations |
| spellingShingle | G. García A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications Applied General Topology Arzelà-Ascoli theorem degree of nondensifiability α-dense curves measures of noncompactness Volterra integral equations |
| title | A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications |
| title_full | A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications |
| title_fullStr | A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications |
| title_full_unstemmed | A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications |
| title_short | A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications |
| title_sort | quantitative version of the arzela ascoli theorem based on the degree of nondensifiability and applications |
| topic | Arzelà-Ascoli theorem degree of nondensifiability α-dense curves measures of noncompactness Volterra integral equations |
| url | https://polipapers.upv.es/index.php/AGT/article/view/10930 |
| work_keys_str_mv | AT ggarcia aquantitativeversionofthearzelaascolitheorembasedonthedegreeofnondensifiabilityandapplications AT ggarcia quantitativeversionofthearzelaascolitheorembasedonthedegreeofnondensifiabilityandapplications |