Relationship of M-/L-convex functions with discrete convex functions by Miller and Favati–Tardella Original Research Article

We clarify the relationship of the concepts of M-convex and L-convex functions due to Murota (Adv. Math. 124 (1996); Math. Programming 83 (1998)) with two other concepts of discrete convex functions over integer lattice points, discretely-convex functions due to Miller (SIAM J. Appl. Math. 21 (1971)), and integrally-convex functions due to Favati–Tardella (Ricerca Operativa 53 (1990)). We also investigate whether each class of discrete convex functions is closed under fundamental operations such as addition and convolution.