On the stability of a generalization of Jensen functional equation (Q1705203)

The author uses the fixed point method to prove the stability and the hyperstability of a generalization of Jensen functional equation \[ \sum_{k=0}^{n-1}f(x+b_ky)=nf(x) \] in the setting of Banach spaces. Here \(n \geq 2\), \(b_k=\exp(2i\pi k/n)\) for \(0\leq k \leq n-1\).