$a+bx \leq f(x)$ for increasing and convex function $f$
66151
Solving inequality for convex functions.
108704
Help with proof of $|x+y| \geq |x|-|y|$
35857
Characterization of log-convexity
73074
$f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
55866
Convex + Monotone =? Convex
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
48275
$f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
96450
If $f(x)$ is continuous and differentiable function , prove that $f(x) \geq e^{3x}, \forall x \geq 0$
9451
Show bounded and convex function on $\mathbb R$ is constant
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
116851
Show that f(x) is convex
62270
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
87207
Prove that the support function of an arbitrary set $A\subset\mathbb R^n$ is convex
60887
$d_A(x) = \inf_{a \in A} \|x-a\|$ is convex if and only if $A$ is convex