Convex Function

Let $X$ be a convex subset of a real vector space and let $f:X\to \mathcal{R}$ be a function. Then $f$ is called convex if and only if

For all $0\le t\le 1$ and all $x_1,x_2\in X$:

$$f(t{x}_1+(1-t)x_2)\le tf(x_1)+(1-t)f(x_2)$$