Stability and superstability of generalized quadratic ternary derivations on non-Archimedean ternary Banach algebras: a fixed point approach

Abstract

Using fixed point method, we prove the Hyers-Ulam stability and the superstability of generalized quadratic ternary derivations on non-Archimedean ternary Banach algebras. Indeed, we investigate the Hyers-Ulam stability and the superstability of the system of functional equations {f([abc]) = [f(a)b(2)c(2)] + [a(2)f(b)c(2)] + [a(2)b(2)f(c)]; g([abc]) = [g(a)b(2)c(2)] + [a(2)f(b)c(2)] + [a(2)b(2)f(c)]; g(ux + vy) + g(ux - vy) = 2u(2)g(x) + 2v(2)g(y); in non-Archimedean ternary Banach algebras.