Том 71
№ 11

All Issues

Kogut P. I.

Articles: 4
Article (Ukrainian)

$V$-Limit Analysis of Vector-Valued Mappings

Kogut P. I., Rudyanova Т. M.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

On weak compactness of bounded sets in Banach and locally convex spaces

Kogut P. I., Mel'nik V. S.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

High-order asymptotics of a solution of one problem of optimal control over a distributed system with rapidly oscillating coefficients

Kogut P. I.

↓ Abstract   |   Full text (.pdf)

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.