Kogut P. I.
Ukr. Mat. Zh. - 2000. - 52, № 12. - pp. 1661-1675
For an arbitrary net of mappings defined on subsets of the Hausdorff space (X, τ) and acting into a vector topological space (Y, τ) semiordered by a solid cone Λ, we introduce the notion of V-limit. We investigate topological and sequential properties of V-limit mappings and establish sufficient conditions for their existence. The results presented can be used as a basis for the procedure of averaging of problems of vector optimization.
Ukr. Mat. Zh. - 2000. - 52, № 6. - pp. 731-739
We investigate the compactness of one class of bounded subsets in Banach and locally convex spaces. We obtain a generalization of the Banach-Alaoglu theorem to a class of subsets that are not polars of convex balanced neighborhoods of zero.
High-order asymptotics of a solution of one problem of optimal control over a distributed system with rapidly oscillating coefficients
Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 940-948
High-order asymptotics is constructed and justified for optimal control over parabolic systems with rapidly oscillating coefficients in the principal part that describes high-intensity heat transfer processes in inhomogeneous and periodic media. The investigation is based on the use of methods of multiscale asymptotic decomposition and some results of the theory of averaging.