Acta Mathematica Hungarica

, Volume 120, Issue 1, pp 1–8

Hyers-Ulam stability for linear equations of higher orders


DOI: 10.1007/s10474-007-7069-3

Cite this article as:
Brzdęk, J., Popa, D. & Xu, B. Acta Math Hung (2008) 120: 1. doi:10.1007/s10474-007-7069-3


We show that, in the classes of functions with values in a real or complex Banach space, the problem of Hyers-Ulam stability of a linear functional equation of higher order (with constant coefficients) can be reduced to the problem of stability of a first order linear functional equation. As a consequence we prove that (under some weak additional assumptions) the linear equation of higher order, with constant coefficients, is stable in the case where its characteristic equation has no complex roots of module one. We also derive some results concerning solutions of the equation.

Key words and phrases

Hyers-Ulam stabilitylinear functional equationsingle variableBanach space

2000 Mathematics Subject Classification


Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsPedagogical UniversityKrakówPoland
  2. 2.Department of MathematicsTechnical UniversityCluj-NapocaRomania
  3. 3.Department of MathematicsSichuan UniversityChengduP.R.China