THE RELATIONSHIP BETWEEN HUYGENS' AND WILKER'S INEQUALITIES AND FURTHER REMARKS

被引：3

作者：

Chen, Chao-Ping ^{[1
]}

Mortici, Cristinel ^{[2
,3
,4
]}

机构：

[1] Henan Polytechn Univ, Sch Math & Informat, Jiaozuo City 454000, Henan, Peoples R China

[2] Valahia Univ Targoviste, Aleea Sinaia 13, Targoviste RO-130004, Romania

[3] Univ Politehn Bucuresti, Splaiul Independentei 313, RO-060042 Bucharest, Romania

[4] Romania Acad Romanian Scientists, Splaiul Independentei 54, RO-050085 Bucharest, Romania

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2023年 / 17卷 / 01期

关键词：

inequalities; Huygens' inequality; Wilker inequality; Cusa's inequality; CUSA-HUYGENS; PROOF;

D O I：

10.2298/AADM210727012C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：92 / 100

页数：9

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