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.
Acta Mathematica Hungarica
Dong, Y., & Zheng, B. (2016). Local stability of a generalized Cauchy equation in Banach spaces. Acta Mathematica Hungarica, 150 (2), 472-478. https://doi.org/10.1007/s10474-016-0647-5