Generalized Hyers-Ulam Stability of Quadratic Functional Inequality

Abstract

We establish the general solution of the functional inequality $∥f\left(x-y\right)+f\left(y-z\right)+f\left(x-z\right)-3f\left(x\right)-3f\left(y\right)-3f\left(z\right)∥\le ∥f\left(x+y+z\right)∥$ and then investigate the generalized Hyers-Ulam stability of this inequality in Banach spaces and in non-Archimedean Banach spaces.