I'd like to show that functions like [tex]x^a[/tex] with [tex]a > 0[/tex] satisfy the Holder condition on an interval like [0, 1]. That is to say that for any x and y in that interval, then for example,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|x^{\frac{1}{2}} - y^{\frac{1}{2}}| \leq C|x-y|^k[/tex]

for some constants C and k.

What is the trick to proving these sorts of things? For Lipschitz continuity, I remember the trick of using mean value theorems with triangle inequalities. And this this?

I'd appreciate some help. It's been a while since I've done analysis.

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# Proving Holder continuous

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