The power mean and the logarithmic mean

Christopher Olutunde Imoru

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-7

Abstract:

In a very interesting and recent note, Tung-Po Lin [1] obtained the least value q and the greatest value p such that M p < L < M q is valid for all distinct positive numbers x and y where M s = ( x s + y s 2 ) 1 s and L = x − y In x - In y

The object of this paper is to give a simpler proof than Lin's of a more general result. More precisely, the author obtained the classes of functions f α and h α , α ∈ R such that In f α ( t ) − h α ( t ) [ t 1 / α + 1 ] − α > 0 , t > 1.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:718951

DOI: 10.1155/S0161171282000313

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