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

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.