Let $E$ be a reflexive normed space and let $\emptyset\neq K\subseteq E$ closed and convex. Show that then exists for every $x\in E$ a "best approximation" in $K$. Therefore a $y\in K$ with $\|x-y\|=d(x,K):=\inf\{\|x-z\|\colon z\in K\}$
Is additionaly $(E,\|\cdot\|)$ uniformly convex, the...
@MartinSleziak I do not really know, but I guess users asking for these questions most have their question closed. So the "closing-reasons" might be good enough? (But since you used to manage lots of meta posts by retagging/editing, so might be you are the best to make a call).
Let $E$ be a reflexive normed space and let $\emptyset\neq K\subseteq E$ closed and convex. Show that then exists for every $x\in E$ a "best approximation" in $K$. Therefore a $y\in K$ with $\|x-y\|=d(x,K):=\inf\{\|x-z\|\colon z\in K\}$
Is additionaly $(E,\|\cdot\|)$ uniformly convex, the...
