Stability of an additive-quartic functional equation in modular spaces

Abstract

In this paper, we prove the Ulam-Hyers stability of the following additive-quartic functional equation \[ f\left(\frac{u+v}{2}-w\right) +f\left(\frac{v+w}{2}-u\right)+f\left(\frac{w+u}{2}-v\right) =\frac{25}{32}\left(f(u-v)+f(v-w)+f(w-u)\right)-\frac{7}{32}\left(f(v-u)+f(w-v)+f(u-w)\right) \] in modular spaces by using the direct method.