Home Competitions SCHWEITZER 1993 Problem 7
SCHWEITZER 1993 Problem 7
Let H be a Hilbert space over the field of real numbers R \Bbb R R f : H → R f: H \to \Bbb R f : H → R f ( x + y + π z ) + f ( x + 2 z ) + f ( y + 2 z ) + f ( π z ) f(x + y + \pi z) + f(x + \sqrt{2} z) + f(y + \sqrt{2} z) + f (\pi z) f ( x + y + π z ) + f ( x + 2 z ) + f ( y + 2 z ) + f ( π z ) = f ( x + y + 2 z ) + f ( x + π z ) + f ( y + π z ) + f ( 2 z ) = f(x + y + \sqrt{2} z) + f (x + \pi z) + f (y + \pi z) + f(\sqrt{2} z) = f ( x + y + 2 z ) + f ( x + π z ) + f ( y + π z ) + f ( 2 z ) x , y , z ∈ H x , y , z \in H x , y , z ∈ H
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