How do I prove function convexity?
16943
Midpoint-Convex and Continuous Implies Convex
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
116548
How to prove the real value function $f$ is convex on $[a,d]$ if $f$ is convex on both $[a,c]$ and $[b,d]$? ($a<b<c<d$).
158399
Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
150727
Characterization convex function.
5416
How does one prove if a multivariate function is constant?
108704
Help with proof of $|x+y| \geq |x|-|y|$
74608
Convex function as supremum of countably many affine functions
135867
$f(x)=x^3$ is convex nor concave without to derivate
138510
Show f(x) is a Lipschitz function
101690
Is linear function convex or concave?
113922
Proof that the intersection of any finite number of convex sets is a convex set
113594
Convex combination of quasiconvex functions.
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
86305
A secant inequality for convex functions
107321
How to show convexity of a ball in metric space?
54764
Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?