Stability and nonstability of the radical Drygas type functional equation

We introduce and find the general solution of the following radical Drygas type functional equation: \(\begin{aligned} f\left( \root 2l+1 \of {u^{2l+1}+v^{2l+1}}\right) +f\left( \root 2l+1 \of {u^{2l+1}-v^{2l+1}}\right) =2f(u)+f(v)+f(-v) \end{aligned}\) $$\begin{array}{c}\hfill f\left(\sqrt[2l+1]{u^{2l+1}+v^{2l+1}}\right)+f\left(\sqrt[2l+1]{u^{2l+1}-v^{2l+1}}\right)=2f(u)+f(v)+f(-v)\end{array}$$ for all \(u,v\in {\mathbb {R}}\) $u,v\in \mathbb{R}$ , where l is a fixed positive integer. Also, we investigate the Hyers-Ulam stability via Brzdȩk’s fixed point technique.