### Approximation theory

### Daghestan Electronic Mathematical Reports: Issue 5 (2016)

# Stability of solutions of the linear system of functional-difference Ito equations

### UDK: 517.929.4+519.21

### Pages: 25 - 48

### DOI: 10.31029/demr.5.4

The purpose of the article is the description of ideas of N.V. Azbelev that were developed in his works and in the works of his students with respect to research
of questions of stability for the functional-linear systems of Ito difference equations. The questions of the permissibility of some pairs of spaces for linear systems of functional difference equations and moment stability of solutions to linear systems of difference Ito equations with delay were considered. Sufficient conditions for the permissibility of some pairs of spaces and stability with respect to initial data for some equations in terms of the parameters of these equations were obtained.

**Keywords: **
stability of solutions, difference equations of Ito, permissibility of pairs of spaces.