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need to show:

[tex]||w||_p^2+||u||_p^2-2(||u||_p^p)^{\frac{2}{p}-1}\Sigma_i(u(i)^{p-1}w(i)) [/tex]

can be bounded as a function of

[tex] ||w-u||_p^2 [/tex]

where [tex] p\in[2,\infty) [/tex]

work done:

the expressions are equal for p=2, and i suspect that

[tex] ||w||_p^2+||u||_p^2-2(||u||_p^p)^{\frac{2}{p}-1}\Sigma_i(u(i)^{p-1}w(i)) \leq||w-u||_p^2 [/tex]

but i get stuck here. Is there some kind of p-norm inequality I can apply here?

Thank you!

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# Bounding p-norm expression

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