(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find two functions [tex]f, g \in C[0,1][/tex] (i.e. continuous functions on [0,1]) which do not satisfy

[tex]2 ||f||^2_{sup} + 2 ||g||^2_{sup} = ||f+g||^2_{sup} + ||f-g||^2_{sup}[/tex]

(where [tex]|| \cdot ||_{sup}[/tex] is the supremum or infinity norm)

2. Relevant equations

Parallelogram identity: [tex]2||x||^2 + 2||y||^2 = ||x+y||^2 + ||x-y||^2[/tex] holds for any x,y

3. The attempt at a solution

Honestly no idea.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Functions not satisfying parallelogram identity with supremum norm

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