On closed convex set containing the extreme points of the unit ball of $C(X)$
15695
Is ${\rm conv}({\rm ext}((C(X))_1))$ dense in $(C(X))_1$?
25171
Why does a convex set have the same interior points as its closure?
71829
Is closure of convex subset of $X$ is again a convex subset of $X$?
108997
Continuous functions that attain local extrema at every point
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
91123
A convex function is differentiable at all but countably many points
102959
Show that $f$ is convex if and only if $f\left( \sum_{i=1}^m\lambda_ix_i \right) \leq \sum_{i=1}^m\lambda_if(x_i)$
40438
Proving that closed (and open) balls are convex
31548
Proof of "every convex function is continuous"
33310
Proving that the set of limit points of a set is closed
142740
If $\varphi \in E'$ and $A$ is convex and open then $\varphi (A)$ is an open interval
128975
Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$
15924
Convexity and strong lower semicontinuity imply weak lower semicontinuity
116382
Showing convexity of a function with the restriction over an arbitrary line
40905
Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f
112597
Extreme point of unit balls, the complex case
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex