The generalized hyperstability of general linear equations in quasi-Banach spaces
The stability aspects of the general linear equation \(f(ax+by)=Af(x)+Bf(y)\) have been studied intensively. However, as the authors of the present paper point out, some of the recent results may not hold in arbitrary normed spaces. These approaches replace the original space by its completion, which may cause problems when applying fixed point methods. Motivated by this fact, the authors investigate the hyperstability of the above linear equation in quasi-Banach spaces instead of normed spaces. The key tool of the proofs is an extension of the fixed point result of \textit{J. Brzdęk} et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6728--6732 (2011; Zbl 1236.39022)] to \(b\)-metric spaces.
scientific article; zbMATH DE number 6877114
scientific article