加强的Wirtinger不等式及其几何应用  

The strengthened Wirtinger inequality and its geometric applications

作　　者：曾春娜 宾芮 董旭 马磊 ZENG Chunna;BIN Rui;DONG Xu;MA Lei(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;School of Sciences,Guangdong Preschool Normal College in Maoming,Maoming 525000,Guangdong,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]广东茂名幼儿师范专科学校理学院,广东茂名525000

出　　处：《陕西师范大学学报（自然科学版）》2023年第1期55-59,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：重庆市自然科学基金(cstc2020jcyj-msxmX0609);重庆市教育委员会科学技术研究项目(KJQN201900530,KJZD-K202200509);重庆师范大学研究生科研创新项目(YKC21036)。

摘　　要：著名的Wirtinger不等式与诸多经典几何不等式等价或为其推广形式。主要研究了Wirtinger不等式的推广,运用周期函数的性质,获得了一系列加强形式的Wirtinger不等式;作为这些Wirtinger不等式的应用,得到了关于原点对称凸体的Bonnesen型不等式的纯分析的证明。The famous Wirtinger inequality in analysis is equivalent to many classical geometric inequalities or its generalized form.The strengthened Wirtinger inequality is investigated.According to the properties of periodic functions,a series of strengthened Wirtinger inequalities are obtained.As an application of these Wirtinger inequalities,the proof of Bonnesen-type inequality for symmetric convex bodies is obtained.

关 键 词：周期函数 等周不等式 WIRTINGER不等式 BONNESEN型不等式 

分 类 号：O186.2[理学—数学]