CRITERION FOR THE EXPONENTIAL STABILITY OF DISCRETE EVOLUTION FAMILY OVER BANACH SPACES

Abstract

We prove that system ξn+1 = T (1)ξn is uniformly exponentially stable then foreach real number θ  and for each p-periodic sequence z(n) with z(0) =0 the unique solution solution of the Cauchy Problem (T (1), θ , 0) isbounded.