Using the papers [1] and [2] the inequality (1) is given and the author indicates the application of the given inequality on two particular cases. In the context of one of these particular cases we discovered a mean M(a, b) on the segment [a, b] labeled as H(a, b)<M(a, b)<G(a, b), together with a geometric interpretation which is given, according to paper [3], by the relationM=H(A, H).