Eine zur Parallelogrammgleichung äquivalente Ungleichung

Summary.

In this paper it is proved that, for a function $f : G\to E$ mapping from an abelian group G divisible by 2 into an inner product space E, the functional inequality¶¶$\Vert2f(x)+2f(y)-f(x y^{-1})\Vert\leq\Vert f(x y)\Vert \ \ \ (x,y\in G)$¶implies the parallelogram equation¶$f(x y)+f(x y^{-1})-2f(x)-2f(y)=0 \ \ \ (x,y\in G)$.