2019
Том 71
№ 7

All Issues

Klishchuk B. A.

Articles: 2
Article (Russian)

Lower bounds for the volume of the image of a ball

Klishchuk B. A., Salimov R. R.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 6. - pp. 774-785

UDC 517.5
We consider ring $Q$-homeomorphisms with respect to $p$-modulus in the space $\Bbb R^{n}$ as $p>n$. We obtain a lower bound for the volume of the image of a ball under these mappings. We solve the extremal problems of minimization of functionals of the volume of the image of a ball and the area of the image of a sphere.

Brief Communications (Russian)

Theorems on Inclusion for Multivalued Mappings

Klishchuk B. A., Tkachuk M. V., Zelinskii Yu. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 7. - pp. 1003–1005

The paper is devoted to the investigation of some properties of multivalued mappings in Euclidean spaces. Fixed-point theorems are proved for multivalued mappings whose restrictions to a certain subset in the closure of a domain satisfy a “coacute angle condition” or a “strict coacute angle condition.” Similar results for the restrictions of multivalued mappings satisfying certain metric conditions are also obtained.