{"title":"$h$中凸函数著名定理的一些扩展","authors":"Amir Garejelo, Farzollah Mirzapour, Ali Morassaei","doi":"arxiv-2409.02450","DOIUrl":null,"url":null,"abstract":"In this paper, we prove that every continuous $h$-mid-convex with suitable\nconditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem,\nBlumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some extensions from famous theorems for $h$-mid-convex function\",\"authors\":\"Amir Garejelo, Farzollah Mirzapour, Ali Morassaei\",\"doi\":\"arxiv-2409.02450\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove that every continuous $h$-mid-convex with suitable\\nconditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem,\\nBlumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.\",\"PeriodicalId\":501036,\"journal\":{\"name\":\"arXiv - MATH - Functional Analysis\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.02450\",\"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 - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02450","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Some extensions from famous theorems for $h$-mid-convex function
In this paper, we prove that every continuous $h$-mid-convex with suitable
conditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem,
Blumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.
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