Porosity of Generalized Mutually Maximization Problem

Let C be a closed bounded convex subset of a Banach space X with 0 being an interior point of C and p_C(.) be the Minkowski functional with respect to C. A generalized mutually maximization problem is said to be well posed if it has a unique solution (x, z) and every maximizing sequence converges strongly to (x, z). Under the assumption that the modulus of convexity with respect to p_C(.) is strictly positive, we show that the collection of all subsets in the admissible family such that the generalized mutually maximization problem fail to be well-posed is σ - porous in the admissible family. These extend and sharpen some recent results due to De Blasi, Myjak and Papini, Li, Li and Xu, and Ni, etc.