Tkachuk M. V.
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.
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.
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 $C^2$.
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.