Abstract
We present two cyclic inequalities involving the classical $\varGamma$-function of Euler and the (unweighted) power mean $$ M_t(a,b)=\left(\frac{a^t+b^t}{2}\right)^{1/t} \quad (t\neq 0), \quad\ M_0(a,b)=\sqrt{ab} \quad (a,b>0). $$ (I) Let $2\le
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