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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) $.

Eine zur Parallelogrammgleichung äquivalente Ungleichung