Almahalebi, M.; Charifi, A.; Kabbaj, S. Hyperstability of a Cauchy functional equation. (English) Zbl 1413.39052 J. Nonlinear Anal. Optim. 6, No. 2, 127-137 (2015). Summary: The aim of this paper is to offer hyperstability results for the Cauchy functional equation \[ f\bigg(\sum_{i=1}^{n}x_{i}\bigg)=\sum_{i=1}^{n}f(x_{i}) \] in Banach spaces. Namely, we show that a function satisfying the equation approximately must be actually a solution to it. Cited in 17 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 39B62 Functional inequalities, including subadditivity, convexity, etc. 47H14 Perturbations of nonlinear operators 47H10 Fixed-point theorems Keywords:hyperstability; Cauchy equation; fixed point theorem PDFBibTeX XMLCite \textit{M. Almahalebi} et al., J. Nonlinear Anal. Optim. 6, No. 2, 127--137 (2015; Zbl 1413.39052) Full Text: Link