{"title":"模块空间中加法二次函数方程的稳定性","authors":"Abderrahman Baza, Mohamed Rossafi, Choonkil Park","doi":"arxiv-2406.15436","DOIUrl":null,"url":null,"abstract":"Using the direct method, we prove the generalised Hyers-Ulam stability of the\nfollowing functional equation \\begin{equation} \\phi(x+y, z+w)+\\phi(x-y, z-w)-2\n\\phi(x, z)-2 \\phi(x, w)=0 \\end{equation} in modular space satisfying the Fatou\nproperty or $\\Delta_2$-condition.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability of additive-quadratic functional equation in modular space\",\"authors\":\"Abderrahman Baza, Mohamed Rossafi, Choonkil Park\",\"doi\":\"arxiv-2406.15436\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Using the direct method, we prove the generalised Hyers-Ulam stability of the\\nfollowing functional equation \\\\begin{equation} \\\\phi(x+y, z+w)+\\\\phi(x-y, z-w)-2\\n\\\\phi(x, z)-2 \\\\phi(x, w)=0 \\\\end{equation} in modular space satisfying the Fatou\\nproperty or $\\\\Delta_2$-condition.\",\"PeriodicalId\":501502,\"journal\":{\"name\":\"arXiv - MATH - General Mathematics\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - General Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2406.15436\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.15436","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability of additive-quadratic functional equation in modular space
Using the direct method, we prove the generalised Hyers-Ulam stability of the
following functional equation \begin{equation} \phi(x+y, z+w)+\phi(x-y, z-w)-2
\phi(x, z)-2 \phi(x, w)=0 \end{equation} in modular space satisfying the Fatou
property or $\Delta_2$-condition.
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