A radial basis function can be represented as
$$ h(x) = \sum_{i=1}^{N} w_i \exp(-\gamma ||x-m_i||^2) $$
where $w_i$'s are weighs, $\gamma$ is a constant. Is this function convex? As far as I know pretty much any reasonably continous function with hills, bowls can be represented with RBFs of the type above, and couldn't we create a function with many local minima that cannot be convex? But $\exp$ is convex, norm operator is convex, and their linear combination must also be convex.