Abstract
Lyapunov functions are constructed and used to establish that an equilibrium of a scalar nonlinear difference equation is globally stable. General conditions for the local stability of an equilibrium of a difference equation which is described by a nonsmooth function are established. Vector Lyapunov functions are constructed and used to establish conditions for an unstable equilibrium to be globally attractive. These results are useful for applications which use scalar nonlinear difference equations as models. They provide insight into conditions for the global convergence of a scalar iterative process in computation.
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