Stability of a generalized Drygas functional equation via Brzdȩk’s fixed point method

Abstract

Using the Brzdȩk fixed point theorem, we establish the Hyers–Ulam stability of the following generalized Drygas functional equation

$$\begin{aligned} \mathcal {F}(x+\sigma (y))+\mathcal {F}(x+\tau (y))=2\mathcal {F}(x)+\mathcal {F}(\sigma (y))+\mathcal {F}(\tau (y)) \end{aligned}$$

for all \(x,y\in X\), where \(\sigma ,\tau : X\rightarrow X\) are additive isometries.