On Jordan type inequalities for hyperbolic functions

TL;DR

This paper explores inequalities related to hyperbolic functions, providing bounds for functions like (sin x)/x and x/(sinh x), extending the classical Jordan inequality.

Contribution

It introduces new bounds and generalizations for inequalities involving hyperbolic functions, expanding the classical Jordan inequality framework.

Findings

Established new lower and upper bounds for (sin x)/x and x/(sinh x)

Generalized Jordan inequalities for hyperbolic functions

Enhanced understanding of inequalities in trigonometric and hyperbolic contexts

Abstract

This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.