From the characterisation of geometrically convex and geometrically concave functions defined on (0, A] or [A, ∞) with A > 0, by means of their multiplicative conditions, we obtain unified proofs of some known and new inequalities. Functions of class C 2 and strictly increasing on (a, b) fulfil some kind of supermultiplicativity and superadditivity. We have obtained a new constant determining the intervals of sub-and supermultiplicativity for the log function.Mathematics Subject Classification (1991). 26A09, 26A48, 26A51, 26D05, 26D15, 33B15.
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