Sum of convex function and increasing function
55866
Convex + Monotone =? Convex
106845
Why is log-of-sum-of-exponentials $f(x)=\log\left(\sum_{i=1}^n e^ {x_i}\right)$ a convex function for $x \in\mathbb R^n$?
31548
Proof of "every convex function is continuous"
102959
Show that $f$ is convex if and only if $f\left( \sum_{i=1}^m\lambda_ix_i \right) \leq \sum_{i=1}^m\lambda_if(x_i)$
47644
Inequality involving rearrangement: $ \sum_{i=1}^n |x_i - y_{\sigma(i)}| \ge \sum_{i=1}^n |x_i - y_i|. $
30423
interior points and convexity
135219
On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $
23119
An application of Jensen's Inequality
6335
Proving that the set enclosed by an ellipse is convex
125175
convexity proof of a function including ln and sums
114184
Show: $\sum_{k=1}^{\infty}\mu(\left\{f\geq k\right\})\leq\int f\, d\mu\leq\sum_{k=0}^{\infty}\mu(\left\{f>k\right\})$
41930
Mean of $ \sum (X_i - \bar{X})^2$
66151
Solving inequality for convex functions.
41876
Finding an asymptotic for the sum $\sum_{p\leq x}p^m$
85153
Show that $f(x) = -\ln(x)$ is convex (WITHOUT using second derivative!)
91131
Question regarding an inequality
54764
Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?