| $\beta$-Homogeneous次的$F$-空间上正交可加的稳定性 |
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| 引用本文： | 刘琪,付林林,黎永锦.$\beta$-Homogeneous次的$F$-空间上正交可加的稳定性[J].数学研究及应用,2022,42(3):289-296. |
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| 作者姓名： | 刘琪 付林林 黎永锦 |
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| 作者单位： | 中山大学数学学院, 广东 广州 510275 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11971493; 12071491), 高校基本科研业务费专项资金(Grant No.2021qntd21). |
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| 摘 要： | 在本文中我们研究了正交?程的稳定性, 其与Wlodzimierz Fechner和Justyna Sikorska在2010年得出的结果密切相关. 本文的差异性在于考虑目标空间赋予$\beta$-齐次范数和拟范数. 通过克服$\beta$-齐次范数和拟范数的瓶颈,得到了新的结果.
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| 关 键 词： | Hyers-Ulam稳定性 $\beta$-齐次的$F$-空间 拟Banach空间 正交可加 |
| 收稿时间： | 2021/3/27 0:00:00 |
| 修稿时间： | 2022/1/11 0:00:00 |
On the Stability of Orthogonal Additivity in $\beta$-Homogeneous $F$-Spaces |
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| Qi LIU,Linlin FU,Yongjin LI.On the Stability of Orthogonal Additivity in $\beta$-Homogeneous $F$-Spaces[J].Journal of Mathematical Research with Applications,2022,42(3):289-296. |
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| Authors: | Qi LIU Linlin FU Yongjin LI |
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| Institution: | Department of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China |
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| Abstract: | In this paper, we study the stability of the orthogonal equation, which is closely related to the results by W. Fechner and J. Sikorska in 2010. There are some differences that we consider the target space with the $\beta$-homogeneous norm and quasi-norm. Overcoming the $\beta$-homogeneous norm and quasi-norm bottlenecks, we get some new results. |
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| Keywords: | Hyers-Ulam stability $\beta$-homogeneous $F$-spaces quasi-Banach spaces orthogonal additivity |
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