Home Competitions Putnam 2012 B5
Prove that, for any two bounded functions g 1 , g 2 : R → [ 1 , ∞ ) g_1, g_2: \mathbb{R} \to [1, \infty) g 1 , g 2 : R → [ 1 , ∞ ) h 1 , h 2 : R → R h_1, h_2: \mathbb{R} \to \mathbb{R} h 1 , h 2 : R → R x ∈ R x \in \mathbb{R} x ∈ R sup s ∈ R ( g 1 ( s ) x g 2 ( s ) ) = max t ∈ R ( x h 1 ( t ) + h 2 ( t ) ) . \sup_{s \in \mathbb{R}} (g_1(s)^x g_2(s)) = \max_{t \in \mathbb{R}} (x h_1(t) + h_2(t)). s ∈ R sup ( g 1 ( s ) x g 2 ( s )) = t ∈ R max ( x h 1 ( t ) + h 2 ( t )) .
Curated text Kedlaya Putnam archive . Quoted with source.
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