The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space
The aim of the paper is to introduce the Banach space consisting of real functions defined on a locally compact and countable at infinity metric space and having increments tempered by a modulus of continuity. We are going to provide a condition that is sufficient for the relative compactness in the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/1/11 |
| _version_ | 1797495801163808768 |
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| author | Józef Banaś Rafał Nalepa |
| author_facet | Józef Banaś Rafał Nalepa |
| author_sort | Józef Banaś |
| collection | DOAJ |
| description | The aim of the paper is to introduce the Banach space consisting of real functions defined on a locally compact and countable at infinity metric space and having increments tempered by a modulus of continuity. We are going to provide a condition that is sufficient for the relative compactness in the Banach space in question. A few particular cases of that Banach space will be discussed. |
| first_indexed | 2024-03-10T01:54:46Z |
| format | Article |
| id | doaj.art-2db23ef522c54ad79f609a535b9fd10d |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T01:54:46Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-2db23ef522c54ad79f609a535b9fd10d2023-11-23T12:58:09ZengMDPI AGAxioms2075-16802021-12-011111110.3390/axioms11010011The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric SpaceJózef Banaś0Rafał Nalepa1Department of Nonlinear Analysis, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszow, PolandDepartment of Nonlinear Analysis, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszow, PolandThe aim of the paper is to introduce the Banach space consisting of real functions defined on a locally compact and countable at infinity metric space and having increments tempered by a modulus of continuity. We are going to provide a condition that is sufficient for the relative compactness in the Banach space in question. A few particular cases of that Banach space will be discussed.https://www.mdpi.com/2075-1680/11/1/11modulus of continuityspace of functions with tempered incrementslocally compact metric spacemetric space countable at infinityrelative compactness |
| spellingShingle | Józef Banaś Rafał Nalepa The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space Axioms modulus of continuity space of functions with tempered increments locally compact metric space metric space countable at infinity relative compactness |
| title | The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space |
| title_full | The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space |
| title_fullStr | The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space |
| title_full_unstemmed | The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space |
| title_short | The Space of Functions with Tempered Increments on a Locally Compact and Countable at Infinity Metric Space |
| title_sort | space of functions with tempered increments on a locally compact and countable at infinity metric space |
| topic | modulus of continuity space of functions with tempered increments locally compact metric space metric space countable at infinity relative compactness |
| url | https://www.mdpi.com/2075-1680/11/1/11 |
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