A Complete Normed Space of a Class of Guage Integrable Functions
The space of all gauge integrable functions equipped with the Alexiewicz norm is not a Banach space. This article defines a class of gauge integrable functions that pose a complete normed space under a suitable norm. First, we discuss how the introduced space evolves naturally from the properties of...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2354758 |
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| _version_ | 1832561619347963904 |
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| author | Yassin Alzubaidi |
| author_facet | Yassin Alzubaidi |
| author_sort | Yassin Alzubaidi |
| collection | DOAJ |
| description | The space of all gauge integrable functions equipped with the Alexiewicz norm is not a Banach space. This article defines a class of gauge integrable functions that pose a complete normed space under a suitable norm. First, we discuss how the introduced space evolves naturally from the properties of the gauge integral. Then, we show that this space properly contains the space of all Lebesgue integrable functions. Finally, we prove that it is a Banach space. This result opens the gate for further studies, such as investigating the verity of convergence theorems on the presented space and studying its other properties. |
| format | Article |
| id | doaj-art-2021a58e74ff4737bfa19c5a98f60326 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2021a58e74ff4737bfa19c5a98f603262025-02-03T01:24:36ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2354758A Complete Normed Space of a Class of Guage Integrable FunctionsYassin Alzubaidi0Department of Mathematical SciencesThe space of all gauge integrable functions equipped with the Alexiewicz norm is not a Banach space. This article defines a class of gauge integrable functions that pose a complete normed space under a suitable norm. First, we discuss how the introduced space evolves naturally from the properties of the gauge integral. Then, we show that this space properly contains the space of all Lebesgue integrable functions. Finally, we prove that it is a Banach space. This result opens the gate for further studies, such as investigating the verity of convergence theorems on the presented space and studying its other properties.http://dx.doi.org/10.1155/2022/2354758 |
| spellingShingle | Yassin Alzubaidi A Complete Normed Space of a Class of Guage Integrable Functions Journal of Mathematics |
| title | A Complete Normed Space of a Class of Guage Integrable Functions |
| title_full | A Complete Normed Space of a Class of Guage Integrable Functions |
| title_fullStr | A Complete Normed Space of a Class of Guage Integrable Functions |
| title_full_unstemmed | A Complete Normed Space of a Class of Guage Integrable Functions |
| title_short | A Complete Normed Space of a Class of Guage Integrable Functions |
| title_sort | complete normed space of a class of guage integrable functions |
| url | http://dx.doi.org/10.1155/2022/2354758 |
| work_keys_str_mv | AT yassinalzubaidi acompletenormedspaceofaclassofguageintegrablefunctions AT yassinalzubaidi completenormedspaceofaclassofguageintegrablefunctions |