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We consider a Volterra discrete system with nonlinear perturbation x ( n +1)= A ( n ) x ( n )+ ~ s =0 n B ( n , s ) x ( s )+ g ( n , x ( n ) and obtain necessary and sufficient conditions for stability properties of the zero solution employing the resolvent equation coupled with the variation of parameters formula.
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Khandaker et al. (2002) studied this question.
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