Is that true that the limiting function which is a function series of convex functions is also convex?

Question

Is that true that the limiting function which is a function series of convex functions is also convex?

I'm not sure what is the exact name of this "limiting function" in English, after the German terminology this is "Grenzfunktion" .

I mean this " A sequence of functions $ (f_{n}) $converges uniformly to a limiting function $ f$ on a set $ E $"

Is this maybe the answer to my question?

Proving that a limit of a convex functions is convex

I appreciate any kind of help.

Answer 1

Finite sums of convex functions are convex and pointwise limit of convex functions is convex so the sum of a pointwise convergent series of convex functions is also convex.