Extended a constant part of Redheffer's type inequalities

Yusuke Nishizawa

Abstract


J-L. Li and Y-L. Li \cite{LL2007} gave the following Redheffer's type inequality; \begin{equation*} \frac{ 1 -\left( \frac{x}{\pi} \right)^2 }{ \sqrt{1 + 3 \left( \frac{x}{\pi} \right)^4}} > \frac{\sin{x}}{x} \end{equation*} holds for $0 < x < \pi$, where the constant $3$ is the best possible. In this paper, we establish two inequalities extended the constant part of the above inequality.

Keywords


Redheffer's inequalities; monotonically increasing functions; monotonically decreasing functions; trigonometric functions

References


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DOI: http://dx.doi.org/10.5556/j.tkjm.49.2018.2505

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