On a factorization of mappings with a prescribed behaviour of the Cauchy difference - Ger, Roman (Annales Mathematicae Silesianae, 1994)
We deal with functional congruences of the form f(x+y) - f(x) - f(y) ∈ U + V where U and V are given sets subjected to satisfy some "separability" conditions essentially weaker than that occurring in [4] which proved to be pretty useful especially while investigating various types of Hyers-Ulam stability problems. The goal is to factorize f into a sum of two functions whose Cauchy differences remain in U and V, respectively, or, at least to obtain an approximation of f by such a sum. An application of the newly established result in that spirit is given. Moreover, a stability result for the celebrated cocycle equation is presented and, finally, the behaviour of mappings whose Cauchy differences fall into a given Hamel basis is described.