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.