On Infinitesimal L_ω-smooth Functions.
The aim of this paper is to study smoothness, approximate continuity, and approximate derivative in a nonstandard manner with respect to infinitesimal parameters. The new nonstandard introduced definitions are combined with standard and nonstandard intermediate value property. Particularly, we show...
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| Format: | Article |
| Language: | English |
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Salahaddin University-Erbil
2022-06-01
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| Series: | Zanco Journal of Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://zancoj.su.edu.krd/index.php/JPAS/article/view/98 |
| _version_ | 1828328220854845440 |
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| author | Ibrahim O. Hamad |
| author_facet | Ibrahim O. Hamad |
| author_sort | Ibrahim O. Hamad |
| collection | DOAJ |
| description | The aim of this paper is to study smoothness, approximate continuity, and approximate derivative in a nonstandard manner with respect to infinitesimal parameters. The new nonstandard introduced definitions are combined with standard and nonstandard intermediate value property. Particularly, we show that the existence of continuous and smooth function has the infinitesimal intermediate value property. Moreover, for the same result, we reduce the continuity condition to the infinitesimal intermediate value condition |
| first_indexed | 2024-04-13T20:06:34Z |
| format | Article |
| id | doaj.art-147409ab695047bf911b05740444a771 |
| institution | Directory Open Access Journal |
| issn | 2218-0230 2412-3986 |
| language | English |
| last_indexed | 2024-04-13T20:06:34Z |
| publishDate | 2022-06-01 |
| publisher | Salahaddin University-Erbil |
| record_format | Article |
| series | Zanco Journal of Pure and Applied Sciences |
| spelling | doaj.art-147409ab695047bf911b05740444a7712022-12-22T02:31:58ZengSalahaddin University-ErbilZanco Journal of Pure and Applied Sciences2218-02302412-39862022-06-01343213110.21271/ZJPAS.34.3.4On Infinitesimal L_ω-smooth Functions.Ibrahim O. Hamad0Department of Mathematic, College of Science, Salahaddin University-Erbil, Kurdistan Region, IraqThe aim of this paper is to study smoothness, approximate continuity, and approximate derivative in a nonstandard manner with respect to infinitesimal parameters. The new nonstandard introduced definitions are combined with standard and nonstandard intermediate value property. Particularly, we show that the existence of continuous and smooth function has the infinitesimal intermediate value property. Moreover, for the same result, we reduce the continuity condition to the infinitesimal intermediate value conditionhttps://zancoj.su.edu.krd/index.php/JPAS/article/view/98nonstandard analysisinfinitesimalnearly smoothsmooth derivationintermediate value propertyinfinitesimal intermediate value propertybaire1functions |
| spellingShingle | Ibrahim O. Hamad On Infinitesimal L_ω-smooth Functions. Zanco Journal of Pure and Applied Sciences nonstandard analysis infinitesimal nearly smooth smooth derivation intermediate value property infinitesimal intermediate value property baire1functions |
| title | On Infinitesimal L_ω-smooth Functions. |
| title_full | On Infinitesimal L_ω-smooth Functions. |
| title_fullStr | On Infinitesimal L_ω-smooth Functions. |
| title_full_unstemmed | On Infinitesimal L_ω-smooth Functions. |
| title_short | On Infinitesimal L_ω-smooth Functions. |
| title_sort | on infinitesimal l ω smooth functions |
| topic | nonstandard analysis infinitesimal nearly smooth smooth derivation intermediate value property infinitesimal intermediate value property baire1functions |
| url | https://zancoj.su.edu.krd/index.php/JPAS/article/view/98 |
| work_keys_str_mv | AT ibrahimohamad oninfinitesimallōsmoothfunctions |