{"title":"严格一致的凸性","authors":"K. Goebel, S. Prus","doi":"10.1093/OSO/9780198827351.003.0003","DOIUrl":null,"url":null,"abstract":"Ways to classify and measure convexity of balls are described. Properties like strict convexity, uniform convexity, and squareness are discussed. The main tool, the modulus of convexity of a space, is studied. In the case of uniformly convex spaces, nearest point projections and asymptotic centres of sequences are presented.","PeriodicalId":417325,"journal":{"name":"Elements of Geometry of Balls in Banach Spaces","volume":"284 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Strict and uniform convexity\",\"authors\":\"K. Goebel, S. Prus\",\"doi\":\"10.1093/OSO/9780198827351.003.0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Ways to classify and measure convexity of balls are described. Properties like strict convexity, uniform convexity, and squareness are discussed. The main tool, the modulus of convexity of a space, is studied. In the case of uniformly convex spaces, nearest point projections and asymptotic centres of sequences are presented.\",\"PeriodicalId\":417325,\"journal\":{\"name\":\"Elements of Geometry of Balls in Banach Spaces\",\"volume\":\"284 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Elements of Geometry of Balls in Banach Spaces\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/OSO/9780198827351.003.0003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Elements of Geometry of Balls in Banach Spaces","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/OSO/9780198827351.003.0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ways to classify and measure convexity of balls are described. Properties like strict convexity, uniform convexity, and squareness are discussed. The main tool, the modulus of convexity of a space, is studied. In the case of uniformly convex spaces, nearest point projections and asymptotic centres of sequences are presented.
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