# A Nice Separation of Some Seiffert-Type Means by Power Means

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- International Journal of Mathematics and Mathematical Sciences
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## Abstract

Seiffert has defined two well-known trigonometric means denoted by π« and π― . In a similar way it was defined by Carlson the logarithmic mean β as a hyperbolic mean. Neuman and SΓ‘ndor completed the list of such means by another hyperbolic mean β³ . There are more known inequalities between the means π« , π― , and β and some power means π π . We add to these inequalities two new results obtaining the following nice chain of inequalities π 0 < β < π 1 / 2 < π« < π 1 < β³ < π 3 / 2 < π― < π 2 , where the power means are evenly spaced with respect to their order.

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