The sequential Henstock-Kurzweil delta integral on time scales
In this study, the basic theory of the sequential Henstock-Kurzweil delta integral on time scales will be discussed. First, we give the notion and the elementary properties of this integral; then we show the equivalence of the Henstock-Kurzweil delta integral and the sequential Henstock-Kurzweil del...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0056 |
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| _version_ | 1846171034472939520 |
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| author | Liu Yang Shao Yabin |
| author_facet | Liu Yang Shao Yabin |
| author_sort | Liu Yang |
| collection | DOAJ |
| description | In this study, the basic theory of the sequential Henstock-Kurzweil delta integral on time scales will be discussed. First, we give the notion and the elementary properties of this integral; then we show the equivalence of the Henstock-Kurzweil delta integral and the sequential Henstock-Kurzweil delta integral on time scales. In addition, we consider the Cauchy criterion and the Fundamental Theorems of Calculus. Finally, we prove Henstock’s lemma and give some convergence theorems. As an application, we consider the existence theorem of a kind of functional dynamic equations. |
| format | Article |
| id | doaj-art-493a780169874347ab2407061d07d55f |
| institution | Kabale University |
| issn | 2391-4661 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-493a780169874347ab2407061d07d55f2024-11-11T08:36:16ZengDe GruyterDemonstratio Mathematica2391-46612024-11-01571185610.1515/dema-2024-0056The sequential Henstock-Kurzweil delta integral on time scalesLiu Yang0Shao Yabin1School of Science, Chongqing University of Posts and Telecommunications, Nanan, 400065, Chongqing, P. R. ChinaSchool of Science, Chongqing University of Posts and Telecommunications, Nanan, 400065, Chongqing, P. R. ChinaIn this study, the basic theory of the sequential Henstock-Kurzweil delta integral on time scales will be discussed. First, we give the notion and the elementary properties of this integral; then we show the equivalence of the Henstock-Kurzweil delta integral and the sequential Henstock-Kurzweil delta integral on time scales. In addition, we consider the Cauchy criterion and the Fundamental Theorems of Calculus. Finally, we prove Henstock’s lemma and give some convergence theorems. As an application, we consider the existence theorem of a kind of functional dynamic equations.https://doi.org/10.1515/dema-2024-0056sequential henstock-kurzweil integraltime scalesdelta integralconvergence theoremsfunctional dynamic equations26a3926a4226e70 |
| spellingShingle | Liu Yang Shao Yabin The sequential Henstock-Kurzweil delta integral on time scales Demonstratio Mathematica sequential henstock-kurzweil integral time scales delta integral convergence theorems functional dynamic equations 26a39 26a42 26e70 |
| title | The sequential Henstock-Kurzweil delta integral on time scales |
| title_full | The sequential Henstock-Kurzweil delta integral on time scales |
| title_fullStr | The sequential Henstock-Kurzweil delta integral on time scales |
| title_full_unstemmed | The sequential Henstock-Kurzweil delta integral on time scales |
| title_short | The sequential Henstock-Kurzweil delta integral on time scales |
| title_sort | sequential henstock kurzweil delta integral on time scales |
| topic | sequential henstock-kurzweil integral time scales delta integral convergence theorems functional dynamic equations 26a39 26a42 26e70 |
| url | https://doi.org/10.1515/dema-2024-0056 |
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