All Questions

I am looking for a reference for the following claim: Let $\phi:\mathbb (a,b) \to \mathbb R$ be a continuous function, and let $c \in (a,b)$ be fixed. Suppose that "$\phi$ is convex at $c$". ...

$\newcommand{\R}{\mathbb R}$ Let $f$ be a function from $\R$ to $\R$. It is said that $f$ is midpoint-convex if for any real $x$ and $y$ we have $f(x-y)+f(x+y)\ge2f(x)$ or, equivalently, $f(x+y)-f(x)\...

$\def\anonfunc#1{#1(\cdot)}$Consider two random variables distributed $v\sim \anonfunc G$ and $c \sim \anonfunc F$ with pdfs $\anonfunc g$ and $\anonfunc f$. Let the supports of $c$ and $v$ be $[x,y]$....

To ask this question I was inspired in some words, if I understand well, from the authors of a preprint on arXiv in section 4.1, that I believe that is [1], to ask next question. We consider the ...

A referee of a submitted paper requested details on the statement that $\int_0^a e^{-tx^2}\,dx$ is log-convex in real $t$, for each $a>0$. While there are a number of ways to prove this statement, ...

Suppose you are given a convex function $f: R^d \rightarrow R$. Let us say you are given $x,x' \in R^d$ and $x_1, x_2, \ldots, x_n \in R^d$ such that $$\sum_{i=1}^n (x_i - x') = x - x'.$$ Is it ...