  One of most important issues in quantum information theory concerns
transmission of information through noisy quantum channels. We discuss few
channel characteristics expressed by means of generalized entropies. Such
characteristics can often be dealt in line with more usual treatment based on
the von Neumann entropies. For any channel, we show that the $q$-average output
entropy of degree $q\geq1$ is bounded from above by the $q$-entropy of the
input density matrix. Concavity properties of the $(q,s)$-entropy exchange are
considered. Fano type quantum bounds on the $(q,s)$-entropy exchange are
derived. We also give upper bounds on the map $(q,s)$-entropies in terms of the
output entropy, corresponding to the completely mixed input.
