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Stability for linear Volterra difference equations in Banach spaces. (English) Zbl 1470.39037

Summary: This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived.

MSC:

39A30 Stability theory for difference equations
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