The classes of lower-C1,α functions (0 < α ≤ 1), that is, functions locally representable as a maximum of a compactly parametrized family of continuously differentiable functions with α-Holder derivative, are hereby introduced. These classes form a strictly decreasing sequence from the larger class of lower-C1 towards the smaller class of lower-C2 functions, and can be analogously characterized via perturbed convex inequalities or via appropriate generalized monotonicity properties of their subdifferentials. Several examples are provided and a complete classification is given. © Heldermann Verlag.
|Journal||Journal of Convex Analysis|
|Publication status||Published - 1 Dec 2005|
- α-hypomonotone operator
- α-weakly convex function
- Lower-C function 1,α
- Maximum function