  Recently, in [P. Jizba and J. Korbel, Physica A 444, 2016, 808-827], four
generalized Shannon-Khinchin [GSK] axioms have been proposed and a generalized
entropy which uniquely satisfies the GSK axioms has been derived. In this
comment, we show that the unique class of the entropies derived in the
aforementioned paper is not correct, as it violates the fourth GSK axiom, and
we derive the correct one. Nevertheless, the class of entropies proposed in the
commented paper still can serve as a basis for generalized statistical
mechanics. We propose a new axiomatic system which characterizes the class of
entropies.
