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

International Journal of Mathematics and Mathematical Sciences
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  • Mathematics


Seiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯 . 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 β„³ . There are more known inequalities between the means 𝒫 , 𝒯 , and β„’ and some power means π’œ 𝑝 . We add to these inequalities two new results obtaining the following nice chain of inequalities π’œ 0 < β„’ < π’œ 1 / 2 < 𝒫 < π’œ 1 < β„³ < π’œ 3 / 2 < 𝒯 < π’œ 2 , where the power means are evenly spaced with respect to their order.

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