  Fast radio bursts (FRBs) are millisecond transients of unknown origin(s)
occurring at cosmological distances. Here we, for the first time, show
time-integrated-luminosity functions and volumetric occurrence rates of
non-repeating and repeating FRBs against redshift. The
time-integrated-luminosity functions of non-repeating FRBs do not show any
significant redshift evolution. The volumetric occurrence rates are almost
constant during the past $\sim$10 Gyr. The nearly-constant rate is consistent
with a flat trend of cosmic stellar-mass density traced by old stellar
populations. Our findings indicate that the occurrence rate of non-repeating
FRBs follows the stellar-mass evolution of long-living objects with $\sim$Gyr
time scales, favouring e.g. white dwarfs, neutron stars, and black holes, as
likely progenitors of non-repeating FRBs. In contrast, the occurrence rates of
repeating FRBs may increase towards higher redshifts in a similar way to the
cosmic star formation-rate density or black hole accretion-rate density if the
slope of their luminosity function does not evolve with redshift. Short-living
objects with $\lesssim$ Myr time scales associated with young stellar
populations (or their remnants, e.g., supernova remnants, young pulsars, and
magnetars) or active galactic nuclei might be favoured as progenitor candidates
of repeating FRBs.
