Sharp power means bounds for Neuman-Sándor mean

For a,b>0 with a\not=b, let N(a,b) denote the Neuman-Sándor mean defined by N(a,b)=((a-b)/(2arcsinh((a-b)/(a+b)))) and A_{r}(a,b) denote the r-order power mean. We present the sharp power means bounds for the Neuman-Sándor mean: A_{p_1}(a,b)<N(a,b)\leqA_{p_2}(a,b), where p_1= ((ln2)/(lnln(3+2\surd2))) and p_2=4/3 are the best constants.

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