Show convexity of $f(\exp(t))$ from $f(\sqrt{xy}) \leq 1/2(f(x)+f(y))$
16943
Midpoint-Convex and Continuous Implies Convex
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
66151
Solving inequality for convex functions.
86305
A secant inequality for convex functions
82198
Proving Convexity of Multivariate Function using Conditional Univariate Convexity
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
144001
If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex
28088
When is $f_{xy}(x,y)\neq f_{yx}(x,y)?$
143936
Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$
2848
Convex integral inequality
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
77217
Proof that a coordinate-wise convex function is convex?
52231
Prove or disprove {$\sum_{i=1}^n x_i^2 = 1$} is convex
35867
Squaring sides of an inequality
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
16463
Is the function $\mbox{tr}(XAX')$ convex?