How to prove $f(x_1,\ldots,x_n) = \sum x_i\ln x_i - (\sum x_i )\ln(\sum x_i)$ is convex on R++
125175
convexity proof of a function including ln and sums
119735
Show that $\mathbb{E}(g(T-p)) < \mathbb{E}(g(S-p))$ for any convex function $g$ if $T$ and $S$ are estimators of $p$
36371
Exercise on convex functions
14448
Elementary proof that $|x|^p$ is convex.
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
25017
Why is every $p$-norm convex?
139711
prove this inequality with $\sum\limits_\text{cyc}\sqrt{1-xy}\ge 2$
4498
Proof that $\|fx\| \leq \|f\|\cdot\|x\|$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
108704
Help with proof of $|x+y| \geq |x|-|y|$
122149
How to prove that $\sum_{i<j}(X_i-X_j)^2=n\sum_{i=1}^{n}(X_i-\bar{X})^2$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
116851
Show that f(x) is convex
67454
Show that $\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^n (x_i - \bar{x})(y_i)$.