The relationship between Huygens' and Wilker's inequalities and further remarks

Applicable Analysis and Discrete Mathematics

article

Chao-Ping Chen¹  Cristinel Mortici² 

[1] School of Mathematics and Informatics, ,(Revised 19. 04. 2023.) Henan Polytechnic University, Jiaozuo City 454000, Henan Province;Valahia University of Tˆargovi¸ste, Aleea Sinaia 13, RO-130004 Tˆargovi¸ste, Romania Politehnica University of Bucharest

关键词: Inequalities;    Huygens' inequality;    Wilker inequality;    Cusa's inequality;   

DOI  :  10.2298/AADM210727012C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 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 inequalitiesdepending on a parameter n, where Huygens’ and Wilker’s inequalities areobtained when n = 1 and n = 2, respectively. By exploiting the aboveidea, 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.

【 授权许可】

Unknown