A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions on
In this manuscript, we provide a generalization of the Cauchy integral to appropriate families of real-valued functions defined in [Formula: see text]. The results are motivated by a generalization of regulated functions. The foundational theory for this extended Cauchy integral is developed in deta...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-12-01
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| Series: | Journal of Taibah University for Science |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2023.2174363 |
| _version_ | 1827288110664253440 |
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| author | Jorge E. Macias-Diaz Karolina Baquero-Mariaca |
| author_facet | Jorge E. Macias-Diaz Karolina Baquero-Mariaca |
| author_sort | Jorge E. Macias-Diaz |
| collection | DOAJ |
| description | In this manuscript, we provide a generalization of the Cauchy integral to appropriate families of real-valued functions defined in [Formula: see text]. The results are motivated by a generalization of regulated functions. The foundational theory for this extended Cauchy integral is developed in detail in this self-contained work. We derive some properties for appropriate families of functions and introduce the Cauchy integral for appropriate step functions. Using these results, the integral for generalized regulated functions is presented next together with some basic properties of the generalized Cauchy integral, including the linearity, the non-negativity and the monotonicity properties. Various illustrative examples on the applicability of our theoretical results are provided. |
| first_indexed | 2024-03-10T08:13:22Z |
| format | Article |
| id | doaj.art-1e279e3b56144ea39c27bbab0a72f51e |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-04-24T11:25:17Z |
| publishDate | 2023-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-1e279e3b56144ea39c27bbab0a72f51e2024-04-10T20:17:48ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552023-12-0117110.1080/16583655.2023.2174363A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions onJorge E. Macias-Diaz0Karolina Baquero-Mariaca1Department of Mathematics and Didactics of Mathematics, School of Digital Technologies, Tallinn University, Tallinn, EstoniaFaculty of Sciences, Autonomous University of Aguascalientes, Aguascalientes, MexicoIn this manuscript, we provide a generalization of the Cauchy integral to appropriate families of real-valued functions defined in [Formula: see text]. The results are motivated by a generalization of regulated functions. The foundational theory for this extended Cauchy integral is developed in detail in this self-contained work. We derive some properties for appropriate families of functions and introduce the Cauchy integral for appropriate step functions. Using these results, the integral for generalized regulated functions is presented next together with some basic properties of the generalized Cauchy integral, including the linearity, the non-negativity and the monotonicity properties. Various illustrative examples on the applicability of our theoretical results are provided.https://www.tandfonline.com/doi/10.1080/16583655.2023.2174363Appropriate familiesextended Cauchy integralgeneralized regulated functionsPrimary 26Axx |
| spellingShingle | Jorge E. Macias-Diaz Karolina Baquero-Mariaca A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions on Journal of Taibah University for Science Appropriate families extended Cauchy integral generalized regulated functions Primary 26Axx |
| title | A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions on |
| title_full | A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions on |
| title_fullStr | A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions on |
| title_full_unstemmed | A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions on |
| title_short | A foundational theory of an extended Cauchy integral for generalized regulated real-valued functions on |
| title_sort | foundational theory of an extended cauchy integral for generalized regulated real valued functions on |
| topic | Appropriate families extended Cauchy integral generalized regulated functions Primary 26Axx |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2023.2174363 |
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