Role of twice fréchet-differentiable mappings in general auxiliary problem principle

The approximation-solvability of the following class of nonlinear variational inequality problems (NVIP) based on the general auxiliary problem principle (LAPP) is discussed. Find an element χ* ε K such that (x*), x − x* + f(x) − f(x*) ≥O, for all x ε K, where T : K → E* is a nonlinear mapping from a nonempty closed convex subset K of a reflexive Banach space E into its dual E*, and f : K → R is a continuous convex functional on K.