Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

Abstract EN

We find the greatest value α and the least value β in (1/2, 1) such that the double inequality C(αa+(1-α)b,αb+(1-α)a)0 with a≠b.

Here, T(a,b)=(a-b)/[2 arctan((a-b)/(a+b))] and Ca,b=(a2+b2)/(a+b) are the Seiffert and contraharmonic means of a and b, respectively.