On certain inequalities for hyperbolic and trigonometric functions
type: Item
instance of: scholarly article
title: On certain inequalities for hyperbolic and trigonometric functions
zbMATH Open document ID: 1280.26006
published in: Journal of Mathematical Inequalities
publication date: 2013-10-24T00:00:00Z
full work available at URL: jmi-07-37.pdf
Mathematics Subject Classification ID: 26A06
Mathematics Subject Classification ID: 26D05
Mathematics Subject Classification ID: 26D99
zbMATH DE Number: 6219470
zbMATH Keywords: trigonometric functions
zbMATH Keywords: hyperbolic functions
zbMATH Keywords: inverse functions
author: József Sándor
MaRDI profile type: Publication
OpenAlex ID: W2316904815
DOI: 10.7153/JMI-07-37
review text: The author obtains several inequalities betwen the trigonometric and hyperbolic functions amd their inverses. Typical results are: if \(-1<x<1\) then \(\sin x \arcsin x\geq x^2\) and if \(x\in \mathbb R\) then \(\sinh x \mathrm{ arcsinh }x\geq x^2\). These results are based on a general inequality between a function and its inverse; if \(f\) is a bijection on an interval in \(]0, \infty[\), with \(f(x)/x\) strictly increasing then \(f(x)\geq y \Longrightarrow f(x) f^{-1}(y) \geq xy\).
reviewed by: P. S. Bullen
description: scientific article; zbMATH DE number 6219470