Stability of additive-quadratic functional equation in modular space

Abstract

Using the direct method, we prove the generalised Hyers-Ulam stability of the following functional equation \begin{equation} ϕ(x+y, z+w)+ϕ(x-y, z-w)-2 ϕ(x, z)-2 ϕ(x, w)=0 \end{equation} in modular space satisfying the Fatou property or $\hat{I}{”}_2$-condition.