Comment on “Improved bounds on entropic uncertainty relations”

We provide an analytical proof of the entropic uncertainty relations presented by J. I. de Vicente and J. S\'anchez-Ruiz [Phys. Rev. A 77, 042110 (2008)] and also show that the replacement of Eq. (27) by Eq. (29) in that reference introduces solutions that do not take fully into account the constraints of the problem, which in turn lead to some mistakes in their treatment.