arXiv 1408.22482014-08-10math.CA

On Lazarevic and Cusa type inequalities for hyperbolic functions with two parameters

Zhen-Hang Yang

备注：: 20 pages

英文摘要：

In this paper, by investigating the monotonicity of a function composed of $% \left( \sinh x\right) /x$ and $\cosh x$ with two parameters in $x$ on $% \left( 0,\infty \right) $, we prove serval theorems related to inequalities for hyperbolic functions, which generalize known results and establish some new and sharp inequalities. As applications, some new and sharp inequalities for bivariate means are presented.

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