Die Funktionalgleichung $f(x) + \max \left\{ {f(y),\,f\left( { - y} \right)} \right\} = \max \left\{ {f\left( {x + y} \right),\,y\left( {x - y} \right)} \right\}$

Abstract

Let G be an abelian group. A function f: G → ℝ solves the equation in the title iff it is additive or f(x) = ∣a(x) + p∣ - p, where p ≥ 0 and a: G → ℝ is additive. As an application, the solution of the equation f(x) + g(y) = max {h(x + y), h(x - y)} with three unknown functions f, g, h: G → ℝ can be determined.

Anläβlich eines Aufenthaltes an der Universität Karlsruhe im April 1995.