E. Imani, A. Najati, M. A. Tareeghee
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{"title":"关于Mikusiński泛函方程的类简森形式","authors":"E. Imani, A. Najati, M. A. Tareeghee","doi":"10.1007/s10474-025-01527-1","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the conditional Jensen functional equation\n</p><div><div><span>$$f(x+y)\\ne 0 \\implies 2f\\big(\\frac{x+y}{2}\\big)=f(x)+f(y), \\quad x,y\\in \\mathcal{G}$$</span></div></div><p>\nfor functions <span>\\(f \\colon \\mathcal{G} \\to\\mathcal{V}\\)</span>, where <span>\\((\\mathcal{G},+)\\)</span> and <span>\\((\\mathcal{V},+)\\)</span> are uniquely 2-divisible groups,\nwith <span>\\((\\mathcal{V},+)\\)</span> being abelian. Additionally, we investigate the hyperstability of this\nfunctional equation.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"175 2","pages":"562 - 571"},"PeriodicalIF":0.6000,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Jensen-like form of Mikusiński's functional equation\",\"authors\":\"E. Imani, A. Najati, M. A. Tareeghee\",\"doi\":\"10.1007/s10474-025-01527-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the conditional Jensen functional equation\\n</p><div><div><span>$$f(x+y)\\\\ne 0 \\\\implies 2f\\\\big(\\\\frac{x+y}{2}\\\\big)=f(x)+f(y), \\\\quad x,y\\\\in \\\\mathcal{G}$$</span></div></div><p>\\nfor functions <span>\\\\(f \\\\colon \\\\mathcal{G} \\\\to\\\\mathcal{V}\\\\)</span>, where <span>\\\\((\\\\mathcal{G},+)\\\\)</span> and <span>\\\\((\\\\mathcal{V},+)\\\\)</span> are uniquely 2-divisible groups,\\nwith <span>\\\\((\\\\mathcal{V},+)\\\\)</span> being abelian. Additionally, we investigate the hyperstability of this\\nfunctional equation.</p></div>\",\"PeriodicalId\":50894,\"journal\":{\"name\":\"Acta Mathematica Hungarica\",\"volume\":\"175 2\",\"pages\":\"562 - 571\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-05-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-025-01527-1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-025-01527-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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