Maxim Tkachuk

• National Academy of Sciences of Ukraine

We prove that a locally bounded and differentiable in the sense of Gateaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differentiable in the sense of Lorch.

The aim of this work is to weaken the conditions of monogenity for functions that take values in subspaces of one concrete three-dimensional commutative algebras over the field of complex numbers. The monogenity of the function understood as a combination of its continuity with the existence of a Gato derivative.

The aim of the present work is to weaken the conditions of monogeneity for functions taking values in a given three-dimensional commutative algebra over the field of complex numbers. The monogeneity of a function is understood as a combination of its continuity with the existence of Gâteaux derivative.

УДК 517.54 Послаблено умови моногенності функцій зі значеннями в певній тривимірній комутативній алгебрі над полем комплексних чисел.Під моногенністю мається на увазі неперервність та існування похідної Гато.

The boundary of fiber linear convex bounded domain with smooth boundary is a cohomological sphere.

The aim of this work is to weaken the conditions of monogenity for functions that take values in one concrete three-dimensional commutative algebras over the field of complex numbers. The monogenity of the function understood as a combination of its continuity with the existence of a Gato derivative.

The main goal of the paper is to solve some problems about shadow for the sphere generalized on the case of the ellipsoid. Here, the essence of the problem is to find the the minimal number of non-overlapping balls with centers on the sphere which are not holding the center of the sphere and such that every line passing through the center of the sp...

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 mu...

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 multiv...

This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a coacute angle condition" or "a strict coacute angle condition". There also were obtained similar results for res...

The solution of one Zamfiresku's problem was obtained. We discuss the unsolved questions related to the Mizel's problem.

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

We establish a criterion for the local linear convexity of sets in the two-dimensional quaternion space $ {\mathbb{H}^2} $ that are analogs of bounded Hartogs domains with smooth boundary in the two-dimensional complex space $ {\mathbb{C}^2} $ .

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

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