Given a convex function $f : \mathbb R^2 \to \mathbb R$ and real numbers $a$ and $b$, I want to check whether the following function $g : \mathbb R^2 \to \mathbb R$ is convex.
First, I think I should use the lemma below:
So I start to write down g(αx1 + (1-α)y1 , αx2+(1-α)y2)
what I get is like this:
Then I get stuck, the function I get is just too complex and I don't know how to do next. Did I do it in the wrong way? Can anyone give me some hints?