# Ostapenko V. V.

### On the Solution of a Locally Finite System of Linear Inequalities with Graph Structure

Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 568-571

We propose a method for the solution of a locally finite system of linear inequalities that arises in the course of solution of problems of control over resource in networks with generalized Kirchhoff law. We present a criterion for a system of inequalities to have the graph structure.

### Methods for the Elimination of Unknowns from Systems of Linear Inequalities and Their Applications

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 50-56

We study methods for the elimination of an unknown or a group of unknowns from systems of linear inequalities. We justify these methods by using the Helly theorem. The methods considered are applied to the calculation of streams in networks with a generalized conservation law.

### To the problem of continuity of many-valued mappings

Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1519–1525

We study the problem of the upper and lower semicontinuity of the union and intersection for a family of many-valued mappings. We establish new conditions of lower semicontinuity for the intersection of a family of lower semicontinuous mappings.

### Matrix convexity

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 64–69

The notion of a convex set is generalized. In the definition of ordinary convexity, sums of products of vectors and numbers are used. In the generalization considered in this paper, the role of numbers is played by matrices; this is why we call it “matrix convexity.”

*H*-convex sets and integration of many-valued mappings

Ukr. Mat. Zh. - 1987. - 39, № 5. - pp. 588–592

### A certain condition of almost convexity

Ukr. Mat. Zh. - 1983. - 35, № 2. - pp. 169—172

### Topological nilgroups of matrices

Ukr. Mat. Zh. - 1980. - 32, № 2. - pp. 175 - 178

### Linear topological N-groups

Ukr. Mat. Zh. - 1978. - 30, № 3. - pp. 400– 403