Two multi-cubic functional equations and some results on the stability in modular spaces
Abstract In this article, we study n-variable mappings which are cubic in each variable. We also show that such mappings can be described by an equation, say, multi-cubic functional equation. Furthermore, we study the stability of such functional equations in the modular space Xρ $X_{\rho }$ by appl...
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2020-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-019-2274-5 |
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doaj-9bddfd591251419fa769feda729f9bd82021-01-10T12:05:01ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-01-012020111610.1186/s13660-019-2274-5Two multi-cubic functional equations and some results on the stability in modular spacesChoonkil Park0Abasalt Bodaghi1Research Institute for Natural Sciences, Hanyang UniversityDepartment of Mathematics, Garmsar Branch, Islamic Azad UniversityAbstract In this article, we study n-variable mappings which are cubic in each variable. We also show that such mappings can be described by an equation, say, multi-cubic functional equation. Furthermore, we study the stability of such functional equations in the modular space Xρ $X_{\rho }$ by applying Δ2 $\Delta _{2}$-condition and the Fatou property (in some cases) on the modular function ρ. Finally, we show that, under some mild conditions, one of these new multi-cubic functional equations can be hyperstable.https://doi.org/10.1186/s13660-019-2274-5Modular space(Multi)-cubic functional equationHyers–Ulam stability |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Choonkil Park Abasalt Bodaghi |
| spellingShingle |
Choonkil Park Abasalt Bodaghi Two multi-cubic functional equations and some results on the stability in modular spaces Journal of Inequalities and Applications Modular space (Multi)-cubic functional equation Hyers–Ulam stability |
| author_facet |
Choonkil Park Abasalt Bodaghi |
| author_sort |
Choonkil Park |
| title |
Two multi-cubic functional equations and some results on the stability in modular spaces |
| title_short |
Two multi-cubic functional equations and some results on the stability in modular spaces |
| title_full |
Two multi-cubic functional equations and some results on the stability in modular spaces |
| title_fullStr |
Two multi-cubic functional equations and some results on the stability in modular spaces |
| title_full_unstemmed |
Two multi-cubic functional equations and some results on the stability in modular spaces |
| title_sort |
two multi-cubic functional equations and some results on the stability in modular spaces |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1029-242X |
| publishDate |
2020-01-01 |
| description |
Abstract In this article, we study n-variable mappings which are cubic in each variable. We also show that such mappings can be described by an equation, say, multi-cubic functional equation. Furthermore, we study the stability of such functional equations in the modular space Xρ $X_{\rho }$ by applying Δ2 $\Delta _{2}$-condition and the Fatou property (in some cases) on the modular function ρ. Finally, we show that, under some mild conditions, one of these new multi-cubic functional equations can be hyperstable. |
| topic |
Modular space (Multi)-cubic functional equation Hyers–Ulam stability |
| url |
https://doi.org/10.1186/s13660-019-2274-5 |
| work_keys_str_mv |
AT choonkilpark twomulticubicfunctionalequationsandsomeresultsonthestabilityinmodularspaces AT abasaltbodaghi twomulticubicfunctionalequationsandsomeresultsonthestabilityinmodularspaces |
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