The stability of \ the fixed points of discrete dynamical systems (DDS) in \ the \ semilinear space $conv(\Bbb R^n)$ (the space of nonempty convex compact sets of $\Bbb R^n$) is investigated. Equation \ in variations in the neighborhood of the fixed point of DDS is derived. Based on the results of the spectral theory of linear operators in Banach space, the conditions \ of localization of the spectrum are obtained. Examples of DDS in $conv(\Bbb R^n)$ for which the stability conditions of the fixed points are reduced to the Schur-Cohn \ criterion for polynomials are considered.

}, keywords = {52A39, 93D30}, isbn = {1083-2564}, doi = {10.12732/caa.v22i2.4}, url = {https://www.acadsol.eu/en/articles/22/2}, author = {V.I. SLYN{\textquoteright}KO and V.S. DENYSENKO and I.V. ATAMAS} }