Korovkin approximation of non-convex set-valued continuous functions

In this paper, we continue the study of Korovkin approximation in cones of Hausdorff continuous set-valued functions. Besides some general results in the context of set-valued functions with compact and convex values, we consider for the first time the possibility of lacking the convex assumption using different methods, namely parametrizations and starshaped conditions. The interest of the new results consist also in considering local conditions which depend on directions of \({\mathbb R}^d\).