Stability of quadratic functional equation in modular spaces

Abstract

In this paper, we study the Hyers-Ulam stability of the following equation \begin{multline*} ϕ(x+y-z)+ϕ(x+z-y)+ϕ(y+z-x)=ϕ(x-y)+ϕ(x-z)+ϕ(z-y) +ϕ(x)+ϕ(y) +ϕ(z) \end{multline*} in modular space, with or without $\hat{I}{”}_2$-condition, and in ${\hat{I}}^2$-homogeneous Banach space.