Abstract. In the paper, we investigate the Hyers–Ulam stability theorem of an Euler–Lagrange additive functional inequality ∥ Xn j=1hXnk=jλkf(xj − xj−1)∥ ≤ ∥fXn j=1λjxj ∥ + φ(x1, · · · , xn), where x0 ≡ 0, n ≥ 3, subject to control function φ in (non-Archimedean) Banach spaces.