Nearly Derivations on Banach Algebras

Abstract

Let 𝑛 be a fixed integer greater than 3 and let 𝜆 be a real number with 𝜆≠(𝑛2−𝑛+4)/2. We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖∑1≤𝑖<𝑗≤𝑛1≤𝑘𝑙≠𝑖,𝑗≤𝑛𝑓((𝑥𝑖+𝑥𝑗∑)/2+𝑛−2𝑙=1𝑥𝑘𝑙∑)+𝑓(𝑛𝑖=2𝑥𝑖)+𝑓(𝑥1∑)‖≤‖𝜆𝑓(𝑛𝑖=1𝑥𝑖)‖.