Jordan Type Inequalities for Hyperbolic Functions and Their Applications

الملخص EN

We present the best possible parameters p, q ∈ 0 , ∞ such that the double inequality 1 / 3 p 2 c o s h ( p x ) + 1 - 1 / 3 p 2 < s i n h ( x ) / x < 1 / 3 q 2 c o s h ( q x ) + 1 - 1 / 3 q 2 holds for all x ∈ 0 , ∞ .

As applications, some new inequalities for certain special function and bivariate means are found.