On generalization of D'Aurizio-Sándor trigonometric inequalities with a parameter

Abstract

In this work, we generalize the D'Aurizio-Sándor inequalities (\cite{D'Aurizio,Sandor}) using an elementary approach. In particular, our approach provides an alternative proof of the D'Aurizio-Sándor inequalities. Moreover, as an immediate consequence of the generalized D'Aurizio-Sándor inequalities, we establish the D'Aurizio-Sándor-type inequalities for hyperbolic functions.