Abstract
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.
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Ukrainian Academy of the Water Industry, Rovno. Translated from Ukrainskii Matematicheskii zhurnal, Vol. 49, No. 7, pp. 970–980. July, 1997.
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Slyusarchuk, V.E. Nonlinear difference equations with asymptotically stable solutions. Ukr Math J 49, 1089–1101 (1997). https://doi.org/10.1007/BF02528754
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DOI: https://doi.org/10.1007/BF02528754