That looks like basically a multiplication (or division) of variables (expressions), which is non-convex. Your only hope of using this in CVX is if there is some reformulation to not form g_k explicitly, but rather refromulate or “smudge” it into something else; but that seems rather unlikely.
@Greeny Please carefully read
Why isn't CVX accepting my model? READ THIS FIRST! .
Your posts repeatedly violate the guidance therein. You will find elaboration on the guidance from @jackfsuia in that link.