Nonlinear Random Stability via Fixed-Point Method

Abstract

We prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation $f\left(x+2y\right)+f\left(x-2y\right)=4f\left(x+y\right)+4f\left(x-y\right)-6f\left(x\right)+f\left(2y\right)+f\left(-2y\right)-4f\left(y\right)-4f\left(-y\right)$ in various complete random normed spaces.