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f^2(x+y) >= f^2(x)+2f(xy)+f^2(y)

Source: ARO 2005 - problem 11.5

April 30, 2005
functioninequalitiesalgebra unsolvedalgebra

Problem Statement

Do there exist a bounded function f:R→Rf: \mathbb{R}\to\mathbb{R} such that f(1)>0f(1)>0 and f(x)f(x) satisfies an inequality f2(x+y)≥f2(x)+2f(xy)+f2(y)f^2(x+y)\ge f^2(x)+2f(xy)+f^2(y)?
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