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generalized Hyers–Ulam stability
Open AccessArticleStability of Euler-Lagrange additive inequality in Banach spaces
Mi Hyun Han*, Hark-Mahn Kim, John Michael Rassias and Eunyoung Son
Annals of Communications in Mathematics ,
(2026),
In Press
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.