2019
Том 71
№ 11

All Issues

Tkachuk M. V.

Articles: 4
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.

Article (Ukrainian)

On some criteria of convexity for compact sets

Tkachuk M. V., Vyhovs'ka I. Yu., Zelinskii Yu. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 466-471

We establish some criteria of convexity of compact sets in the Euclidean space. Analogs of these results are extended to complex and hypercomplex cases.

Article (Ukrainian)

Analytic criterion for linear convexity of Hartogs domains with smooth boundary in $H^2$

Osipchuk T. M., Tkachuk M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 226-236

We establish a criterion of the local linear convexity of sets in the two-dimensional quaternion space $H^2$, that are similar to the bounded Hartogs domains with smooth boundaries in the two-dimensional complex space $C^2$.

Brief Communications (Ukrainian)

Besicovitch-Danzer-type characterization of a circle

Tkachuk M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 6. - pp. 862–864

We investigate a Besicovitch-Danzer-type characterization of a circle in a class of compact sets whose boundary divides the plane into several components.