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

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.