Uniform convexity requires stronger triangle inequality to be true uniformly.
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From the wikipedia (in the section "Properties") https://en.wikipedia.org/wiki/Uniformly_convex_space : The strict convexity means a stronger triangle inequality $|x+y|<|x|+|y|$ holds whenever x,y are linearly independent, while the uniform convexity requires this inequality to be true uniformly.
I don't understand the last statement i.e. "the uniform convexity requires this inequality to be true uniformly."
functional-analysis banach-spaces normed-spaces
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
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add a comment |
$begingroup$
From the wikipedia (in the section "Properties") https://en.wikipedia.org/wiki/Uniformly_convex_space : The strict convexity means a stronger triangle inequality $|x+y|<|x|+|y|$ holds whenever x,y are linearly independent, while the uniform convexity requires this inequality to be true uniformly.
I don't understand the last statement i.e. "the uniform convexity requires this inequality to be true uniformly."
functional-analysis banach-spaces normed-spaces
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
$endgroup$
$begingroup$
You might want to give a link to the Wiki page.
$endgroup$
– copper.hat
Dec 9 '18 at 6:05
add a comment |
$begingroup$
From the wikipedia (in the section "Properties") https://en.wikipedia.org/wiki/Uniformly_convex_space : The strict convexity means a stronger triangle inequality $|x+y|<|x|+|y|$ holds whenever x,y are linearly independent, while the uniform convexity requires this inequality to be true uniformly.
I don't understand the last statement i.e. "the uniform convexity requires this inequality to be true uniformly."
functional-analysis banach-spaces normed-spaces
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
$endgroup$
From the wikipedia (in the section "Properties") https://en.wikipedia.org/wiki/Uniformly_convex_space : The strict convexity means a stronger triangle inequality $|x+y|<|x|+|y|$ holds whenever x,y are linearly independent, while the uniform convexity requires this inequality to be true uniformly.
I don't understand the last statement i.e. "the uniform convexity requires this inequality to be true uniformly."
functional-analysis banach-spaces normed-spaces
functional-analysis banach-spaces normed-spaces
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
edited Dec 9 '18 at 6:19
Infinity
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
asked Dec 9 '18 at 6:01
InfinityInfinity
622514
622514
$begingroup$
You might want to give a link to the Wiki page.
$endgroup$
– copper.hat
Dec 9 '18 at 6:05
add a comment |
$begingroup$
You might want to give a link to the Wiki page.
$endgroup$
– copper.hat
Dec 9 '18 at 6:05
$begingroup$
You might want to give a link to the Wiki page.
$endgroup$
– copper.hat
Dec 9 '18 at 6:05
$begingroup$
You might want to give a link to the Wiki page.
$endgroup$
– copper.hat
Dec 9 '18 at 6:05
add a comment |
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– copper.hat
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