Proving that an ellipsoid is convex
56081
Prove that the ellipsoid $E = \{ (x,y,z) \in R^3 \mid \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} \leq 1 \}$ is convex
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
8963
Function that is both midpoint convex and concave
71975
Showing that an Isometry on the Euclidean Plane fixing the origin is Linear
30572
Intersection of nested closed bounded convex sets in Euclidean space
95250
Proof a special extension on the isoperimetric theorem
107321
How to show convexity of a ball in metric space?
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$
142862
Intersection of an ellipsoid and plane in parametric form
74608
Convex function as supremum of countably many affine functions
143936
Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$
122305
Proof of matrix norm property: submultiplicativity
142922
How to prove that $e^x$ is convex?
83449
Proof with 3D vectors
9138
Projection of a point onto a simple convex polytope
85153
Show that $f(x) = -\ln(x)$ is convex (WITHOUT using second derivative!)
96590
Convex cyclic hexagon $ABCDEF$. Prove $AC \cdot BD \cdot CE \cdot DF \cdot AE \cdot BF \geq 27 AB \cdot BC \cdot CD \cdot DE \cdot EF \cdot FA$