詹森型几何形状

IF 0.1 Q4 MATHEMATICS

Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica Pub Date : 2018-04-10 DOI:10.2478/aupcsm-2020-0002

P. Pasteczka

{"title":"詹森型几何形状","authors":"P. Pasteczka","doi":"10.2478/aupcsm-2020-0002","DOIUrl":null,"url":null,"abstract":"\n We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary.\n It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.","PeriodicalId":53863,"journal":{"name":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","volume":"7 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2018-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Jensen-type geometric shapes\",\"authors\":\"P. Pasteczka\",\"doi\":\"10.2478/aupcsm-2020-0002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary.\\n It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.\",\"PeriodicalId\":53863,\"journal\":{\"name\":\"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2018-04-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/aupcsm-2020-0002\",\"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":"Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/aupcsm-2020-0002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 8

摘要

我们给出了凸闭合形状的充分必要条件，使得对于每一个凸函数，该形状上的平均积分不超过其边界上的平均积分。证明了该不等式适用于n维平行四边形、n维球和具有圆心在其边界质心处的内切球(与其所有面相切)的凸多面体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Jensen-type geometric shapes

We present both necessary and sufficient conditions for a convex closed shape such that for every convex function the average integral over the shape does not exceed the average integral over its boundary. It is proved that this inequality holds for n-dimensional parallelotopes, n-dimensional balls, and convex polytopes having the inscribed sphere (tangent to all its facets) with the centre in the centre of mass of its boundary.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica MATHEMATICS-

自引率

11.10%

发文量

审稿时长

15 weeks