This talk describes fundamental properties of M-convex and L-convex functions that play the central roles in discrete convex analysis.
These concepts were originally introduced in combinatorial optimization, but turned out to be relevant in economics.
Emphasis is put on discrete duality and conjugacy respect to the Legendre-Fenchel transformation.

Monograph information: 
http://www.misojiro.t.u-tokyo.ac.jp/~murota/mybooks.html#DCAsiam200