Asymptotic behavior of discrete evolution families in Banach spaces

Abstract

Let X be a Banach space, be an operator-valued sequence and let be the discrete evolution family associated to In this paper we prove that the family is non-uniformly strongly stable (i.e. for every nonnegative integer m and every if and only if it is -approximative admissible, i.e. for every sequence in and every positive number there exists the sequence in satisfying such that the solution of the discrete Cauchy Problem belongs to Other types of asymptotic behavior of the family are also analyzed.

Keywords:

• Non-autonomous difference equations
• discrete evolution families of bounded linear operators
• discrete evolution semigroups
• boundedness and asymptotic stability

AMS Subject Classifications:

• Primary 35B35

Notes

No potential conflict of interest was reported by the authors.