2019
Том 71
№ 9

All Issues

Skvortsov S. A.

Articles: 2
Article (Russian)

On the equicontinuity of families of mappings in the case of variable domains

Sevost'yanov E. A., Skvortsov S. A.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 7. - pp. 938-951

UDC 517.5
We study the problem of local behavior of maps in the closure of a domain in the Euclidean space. The equicontinuity of families of these mappings is established in the case where the mapped domain is not fixed. We separately consider the domains with bad and good boundaries, as well as the homeomorphisms and maps with branching.

Article (Russian)

On convergence of mappings in metric spaces with direct and inverse modulus conditions

Sevost'yanov E. A., Skvortsov S. A.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 7. - pp. 952-687

For mappings in metric spaces satisfying one inequality with respect to the modulus of families of curves, we establish the property of lightness of the limit mapping. It is shown that the uniform limit of these mappings is a light mapping, whenever the function responsible for the distortion of the families of curves, is of finite mean oscillation at every point. In addition, for one class of homeomorphisms of metric spaces, we prove theorems on the equicontinuity of the families of inverse mappings.