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

Abstract

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.

17 pages

References in corpus (4)

• New sharp Jordan type inequalities and their applications
• Sharp bounds for the second Seiffert mean in terms of power means
• The monotonicity results and sharp inequalities for some power-type means of two arguments
• Refinements of Mitrinović-Cusa inequality