{"title":"中值定理和凸性:两个数学项目相互作用的一个例子","authors":"J. Hiriart-Urruty","doi":"10.4171/em/406","DOIUrl":null,"url":null,"abstract":". With the help of two types of results, one for real-valued functions, the other one for vector-valued functions, we show how the classical mean value theorems (in an equality form) and the concept of convexity (for functions and for sets) are closely related.","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":"19 4","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/em/406","citationCount":"1","resultStr":"{\"title\":\"Mean value theorems and convexity: An example of cross-fertilization of two mathematical items\",\"authors\":\"J. Hiriart-Urruty\",\"doi\":\"10.4171/em/406\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". With the help of two types of results, one for real-valued functions, the other one for vector-valued functions, we show how the classical mean value theorems (in an equality form) and the concept of convexity (for functions and for sets) are closely related.\",\"PeriodicalId\":41994,\"journal\":{\"name\":\"Elemente der Mathematik\",\"volume\":\"19 4\",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2020-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/em/406\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Elemente der Mathematik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/em/406\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Elemente der Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/em/406","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Mean value theorems and convexity: An example of cross-fertilization of two mathematical items
. With the help of two types of results, one for real-valued functions, the other one for vector-valued functions, we show how the classical mean value theorems (in an equality form) and the concept of convexity (for functions and for sets) are closely related.