The q-asymptotic function in c-convex analysis

We establish several connections between generalized asymptotic functions and different areas of convexity theory, without coercivity assumptions. Properties and characterizations of abstract subdifferentials, normal cones, conjugates, support functions and optimality conditions for the minimization problem are given. We provide a new result on existence of minimizers for a class of nonconvex functions which is strictly larger than the class of quasiconvex ones.