Is the positive linear combinations of pseudoconvex functions pseudoconvex?

Question

Let $f_i$ be pseudoconvex functions for $i=1,\cdots, n$ and let $a_i$ be positive reals.

Is the function $f = \sum_{i=1}^n f_i$ pseudoconvex?

Thanks in advance

Answer 1

Take $f_1(x) = -x^3 - x$ and $f_2(x) = 2x^3 + x$. The sum is $f(x) = x^3$ which is not pseudoconvex ($x=0$, $y=-1$ is a counterexample in the Wikipedia definition).