Suppose that X be a reflexive Banach space and function $f:X×X↦R$ which is concave in its first argument and convex in its second one. How to prove $f(x,x)=0$ for all $x∈X$?
$f$ is concave and convex in its arguments.
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functional-analysis
convex-analysis
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2What about $f(x,x) = 1$? – 2012-12-24