Sub- and superadditive properties of Euler's gamma function

Let center dot center dot 0 and 0 center dot center dot not equal 1 be real numbers. The inequality (GRAPHICS) holds for all positive real numbers center dot center dot center dot if and only if center dot >= max( 1 center dot center dot). The reverse inequality is valid for all center dot center dot center dot center dot 0 if and only if center dot <= min( 1 center dot center dot).