A fixed point approach to the hyperstability of the general linear equation in \(\beta\)-Banach spaces (Q1653425)

The authors firstly reformulate the fixed point theorem of \textit{J. Brzdęk} et al. (see Theorem 1 of [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6728--6732 (2011; Zbl 1236.39022)]) in \(\beta\)-Banach spaces. Their main results state that, under some assumptions, functions satisfying the general linear equation \[ f(ax+by)=rf(x)+sf(y) \qquad \left(x, y\in X\right) \] only approximately (in some sense), must actually be solutions to it.