Nonlinear difference equations with asymptotically stable solutions
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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.
KeywordsBanach Space Difference Equation Asymptotic Stability Trivial Solution Spectral Radius
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