Local stability of a generalized Cauchy equation in Banach spaces


Let (G, ·) be a group and E be a Banach space. Assume that f: G→ E is a map such that f(G) is an open set containing 0. If there exists an ε> 0 and a p > 1 so that (Formula Presented.) for all x, y∈ G, then f is an additive map onto E. If E is a finite-dimensional Banach space, the result holds when f(G) (not necessarily open) contains 0 as an interior point.

Publication Title

Acta Mathematica Hungarica