{"title":"关于ev定理的一个特殊推广","authors":"V. Cîrtoaje, L. Giugiuc","doi":"10.37193/cmi.2022.02.03","DOIUrl":null,"url":null,"abstract":"The main aim of the paper is to determine the extreme values of the product $P=a_1a_2\\cdots a_n$ under the constraints $\\sum_{i=1}^n a_i=S$ and $\\sum_{i=1}^{n}\\frac 1{a_i+1}=S_0$ for $n\\ge 3$ nonnegative real numbers $a_1,a_2,\\ldots, a_n$ and some given constants $S$ and $S_0$. Some interesting applications of our results are provided as well.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a particular extension of the EV-Theorem\",\"authors\":\"V. Cîrtoaje, L. Giugiuc\",\"doi\":\"10.37193/cmi.2022.02.03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The main aim of the paper is to determine the extreme values of the product $P=a_1a_2\\\\cdots a_n$ under the constraints $\\\\sum_{i=1}^n a_i=S$ and $\\\\sum_{i=1}^{n}\\\\frac 1{a_i+1}=S_0$ for $n\\\\ge 3$ nonnegative real numbers $a_1,a_2,\\\\ldots, a_n$ and some given constants $S$ and $S_0$. Some interesting applications of our results are provided as well.\",\"PeriodicalId\":112946,\"journal\":{\"name\":\"Creative Mathematics and Informatics\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Creative Mathematics and Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37193/cmi.2022.02.03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Creative Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37193/cmi.2022.02.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The main aim of the paper is to determine the extreme values of the product $P=a_1a_2\cdots a_n$ under the constraints $\sum_{i=1}^n a_i=S$ and $\sum_{i=1}^{n}\frac 1{a_i+1}=S_0$ for $n\ge 3$ nonnegative real numbers $a_1,a_2,\ldots, a_n$ and some given constants $S$ and $S_0$. Some interesting applications of our results are provided as well.
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