  Metrization of statistical divergences is useful in both theoretical and
practical aspects. Considering the fractional powers of statistical divergences
is one way to obtain metrics associated with divergences. With this motivation,
Os\'an, Bussandri, and Lamberti (2018) considered metrizations for the
fractional powers of the Jensen-Shannon divergences between multinomial
distributions and gave an open problem. In this short note, we give an
affirmative answer to their conjecture. This method is also applicable to
powers of f-divergences between the Cauchy distribution.
