{"title":"幂指数函数的下界","authors":"Yusuke Nishizawa","doi":"10.7153/jca-2019-15-01","DOIUrl":null,"url":null,"abstract":". In this paper, we consider the lower bound of the power exponential function a 2 b + b 2 a for nonnegative real numbers a and b . If a + b = 1, then it is known that the function has the maximum value 1, but it is no known that the minimum value. In this paper, we show that a 2 b + b 2 a > 6083 / 6144 ∼ = 0 . 990072 for nonnegative real numbers a and b with a + b = 1.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A lower bound of the power exponential function\",\"authors\":\"Yusuke Nishizawa\",\"doi\":\"10.7153/jca-2019-15-01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we consider the lower bound of the power exponential function a 2 b + b 2 a for nonnegative real numbers a and b . If a + b = 1, then it is known that the function has the maximum value 1, but it is no known that the minimum value. In this paper, we show that a 2 b + b 2 a > 6083 / 6144 ∼ = 0 . 990072 for nonnegative real numbers a and b with a + b = 1.\",\"PeriodicalId\":73656,\"journal\":{\"name\":\"Journal of classical analysis\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of classical analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/jca-2019-15-01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of classical analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/jca-2019-15-01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. In this paper, we consider the lower bound of the power exponential function a 2 b + b 2 a for nonnegative real numbers a and b . If a + b = 1, then it is known that the function has the maximum value 1, but it is no known that the minimum value. In this paper, we show that a 2 b + b 2 a > 6083 / 6144 ∼ = 0 . 990072 for nonnegative real numbers a and b with a + b = 1.
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