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On nonstability of the linear recurrence of order one

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
367
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2009.12.052
Keywords
  • Hyers–Ulam Stability
  • Nonstability
  • Linear Recurrence
  • Shadowing
  • Banach Space
Disciplines
  • Computer Science

Abstract

Abstract We show that, under some assumptions, the linear recurrence (or difference equation) of order one in a Banach space is nonstable in the Hyers–Ulam sense. Our results are also connected with the notion of shadowing in dynamical systems and computer sciences.

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