Nonlinear difference equations with asymptotically stable solutions
We establish conditions of asymptotic stability for all solutions of the equation X n+1=F(X n ), n≥0, in the Banach space E in the case where r(F′(x))<1 ∀ x ∈ E, r′(x) is the spectral radius of F′(x). An example of an equation with an unstable solution is given.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 7, pp 1089-1101.
Citation Example: Slyusarchuk V. E. Nonlinear difference equations with asymptotically stable solutions // Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 970–980. July.