  Discrete convex functions are used in many areas, including operations
research, discrete-event systems, game theory, and economics. The objective of
this paper is to investigate basic operations such as direct sum, splitting,
and aggregation that are related to network induction of discrete convex
functions as well as discrete convex sets. Various kinds of discrete convex
functions in discrete convex analysis are considered such as integrally convex
functions, L-convex functions, M-convex functions, multimodular functions, and
discrete midpoint convex functions.
