n-SUBDIFFERENTIABILITY OF n-CONVEX FUNCTIONS

In this paper we study n-convex functions. We mainly study four types of n-convex functions: lower semicontinuous n-convex functions, simple n-convex, n(A)-sublinear and n-sublinear functions. We also consider nconvex functions that are the pointwise upper bound of some non-empty family of n-affine, n(A)-affine, n-linear and n(A)-linear functions, respectively. It is shown that n-convex functions are closely related to convex functions defined on the tensor product of spaces. In this paper we study n-subdifferentiability of n-convex functions, simple n-convex, n-sublinear functions and study a number of their properties. In this paper we also study the properties of n-conjugate functions. In this paper we study the n-subdifferential of the maximum function. Using convex hulls of n-convex functions on the tensor product of spaces, criteria for n-subdifferentiability of n-convex functions are obtained. A characterization of n-convex functions and n-convex sets is considered.