Epi-lower semicontinuous mappings and their properties (in Ukrainian)

We present a new concept of lower semicontinuity for vector-valued mappings, so-called lower epi-semicontinuity, which is closely related with the sequential closedness of epigraphs of these mappings. We consider the case when the mappings take values in a real Banach space Y partially ordered by a closed convex pointed cone L, and we make no additional assumptions on topological interior of the ordering cone. We also study the comparison of the lower epi-semicontinuity with the classical notion of lower semicontinuity and its generalizations.