{"title":"惠更斯不等式和威尔克不等式之间的关系以及进一步的评论","authors":"Chao-Ping Chen, C. Mortici","doi":"10.2298/aadm210727012c","DOIUrl":null,"url":null,"abstract":"The first aim of this paper is to show how the Huygens? and Wilker?s inequalities are related. In this sense, we establish and prove a class of inequalities depending on a parameter n, where Huygens? and Wilker?s inequalities are obtained when n = 1 and n = 2, respectively. By exploiting the above idea, we introduce other classes of inequalities depending on a parameter, extending an inequality of Wilker type and also the classical Cusa inequality. Finally, some open problems are posed.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The relationship between Huygens’ and Wilker’s inequalities and further remarks\",\"authors\":\"Chao-Ping Chen, C. Mortici\",\"doi\":\"10.2298/aadm210727012c\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The first aim of this paper is to show how the Huygens? and Wilker?s inequalities are related. In this sense, we establish and prove a class of inequalities depending on a parameter n, where Huygens? and Wilker?s inequalities are obtained when n = 1 and n = 2, respectively. By exploiting the above idea, we introduce other classes of inequalities depending on a parameter, extending an inequality of Wilker type and also the classical Cusa inequality. Finally, some open problems are posed.\",\"PeriodicalId\":51232,\"journal\":{\"name\":\"Applicable Analysis and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Analysis and Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2298/aadm210727012c\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/aadm210727012c","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The relationship between Huygens’ and Wilker’s inequalities and further remarks
The first aim of this paper is to show how the Huygens? and Wilker?s inequalities are related. In this sense, we establish and prove a class of inequalities depending on a parameter n, where Huygens? and Wilker?s inequalities are obtained when n = 1 and n = 2, respectively. By exploiting the above idea, we introduce other classes of inequalities depending on a parameter, extending an inequality of Wilker type and also the classical Cusa inequality. Finally, some open problems are posed.
期刊介绍:
Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).