Advances in Difference Equations
Volume 2005 (2005), Issue 2, Pages 101-107
doi:10.1155/ADE.2005.101
Hyers-Ulam stability of the linear recurrence with constant coefficients
Department of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, 25-38 Gh. Baritiu Street, Cluj-Napoca 3400, Romania
Received 5 November 2004; Revised 14 March 2005
Copyright © 2005 Dorian Popa. 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.
Abstract
Let X be a Banach space over the field ℝ or ℂ, a1,…,ap∈ℂ, and (bn)n≥0 a sequence in X. We investigate the Hyers-Ulam stability of the linear recurrence xn+p=a1xn+p−1+⋯+ap−1xn+1+apxn+bn, n≥0, where x0,x1,…,xp−1∈X.