General Clarkson type inequality
$begingroup$
Let $f: mathbb{R}^n to mathbb{R}$ be a positively p-Homogeneous and convex function for $p geq 2, n geq 2.$
Then how to prove
$2 fleft(frac{x_1+x_2}{2}right) + 2 fleft(frac{x_1-x_2}{2}right) leq f(x_1) +f(x_2)$
functional-analysis convex-analysis
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
$endgroup$
add a comment |
$begingroup$
Let $f: mathbb{R}^n to mathbb{R}$ be a positively p-Homogeneous and convex function for $p geq 2, n geq 2.$
Then how to prove
$2 fleft(frac{x_1+x_2}{2}right) + 2 fleft(frac{x_1-x_2}{2}right) leq f(x_1) +f(x_2)$
functional-analysis convex-analysis
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
$endgroup$
add a comment |
$begingroup$
Let $f: mathbb{R}^n to mathbb{R}$ be a positively p-Homogeneous and convex function for $p geq 2, n geq 2.$
Then how to prove
$2 fleft(frac{x_1+x_2}{2}right) + 2 fleft(frac{x_1-x_2}{2}right) leq f(x_1) +f(x_2)$
functional-analysis convex-analysis
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
$endgroup$
Let $f: mathbb{R}^n to mathbb{R}$ be a positively p-Homogeneous and convex function for $p geq 2, n geq 2.$
Then how to prove
$2 fleft(frac{x_1+x_2}{2}right) + 2 fleft(frac{x_1-x_2}{2}right) leq f(x_1) +f(x_2)$
functional-analysis convex-analysis
functional-analysis convex-analysis
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
asked Dec 19 '18 at 17:30
R.AroraR.Arora
64
64
add a comment |
add a comment |
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