Hennessy, David A.

Journal of Mathematical Analysis and Applications Vol. 225 (September 1998): 340-346.

Inequalities are identified for subadditive (superadditive) functions of supermodular (submodular) functions. A simple adaptation yields inequalities for submultiplicative (supermultiplicative) compositions of log-supermodular (log-submodular) functions. Inequalities are also developed when the order of composition is reversed.