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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 269356, 5 pages
Research Article

Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Received 17 November 2014; Accepted 23 January 2015

Academic Editor: Rigoberto Medina

Copyright © 2015 Bing Xu and Janusz Brzdęk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the Hyers-Ulam stability in a Banach space of the system of first order linear difference equations of the form for (nonnegative integers), where is a given matrix with real or complex coefficients, respectively, and is a fixed sequence in . That is, we investigate the sequences in such that (with the maximum norm in ) and show that, in the case where all the eigenvalues of are not of modulus 1, there is a positive real constant (dependent only on ) such that, for each such a sequence , there is a solution of the system with .