Set-Valued Robust Mappings and Approximatable Mappings

The concepts of robustness of sets and mappings were proposed for the theory of integral global optimization. This paper discusses the robustness of a set-valued mapping, associating with the stability problem. We extend the equivalence between the robustness and the approximatability to the case of a set-valued mapping. We deal also with "bi-robustness" and "in-robustness."