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Unification and refinements of Jordan, Adamović-Mitrinovićand and Cusa's inequalities

In this paper, we find some new sharp bounds for $\left(\sin x\right) /x$, which unify and refine Jordan, Adamović-Mitrinovićand and Cusa's inequalities. As applications of main results, some new Shafer-Fink type inequalities for arc sine function and ones for certain bivariate means are established, and a simpler but more accurate estimate for sine integral is derived.

preprint2013arXivOpen access
Zhen-Hang Yang
math.CA
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Zhen-Hang Yang

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