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Post Closed as "Not suitable for this site" by Benoît Kloeckner, Gerald Edgar, Daniel Moskovich, David White, Suvrit
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Gerald Edgar
Gerald Edgar
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I want to prove the inequality |x-y|^p <= p/2*|x-y|*(x^(p-1)+y^(p-1)) if p>=1 $$ |x-y|^p \le \frac{p}{2}\big|x-y\big|\;\big(x^{p-1}+y^{p-1}\big) $$ if $p \ge 1$. For the case p$p$ is an integer, it's easy to do, but I have no idea when p$p$ is not an integer! Thank you for the answer.

I want to prove the inequality |x-y|^p <= p/2*|x-y|*(x^(p-1)+y^(p-1)) if p>=1 For the case p is an integer, it's easy to do, but I have no idea when p is not an integer! Thank you for the answer.

I want to prove the inequality $$ |x-y|^p \le \frac{p}{2}\big|x-y\big|\;\big(x^{p-1}+y^{p-1}\big) $$ if $p \ge 1$. For the case $p$ is an integer, it's easy to do, but I have no idea when $p$ is not an integer! Thank you for the answer.

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Chen Jie
Chen Jie
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a inequality of $L^p$

I want to prove the inequality |x-y|^p <= p/2*|x-y|*(x^(p-1)+y^(p-1)) if p>=1 For the case p is an integer, it's easy to do, but I have no idea when p is not an integer! Thank you for the answer.