  Risaliti and Lusso have compiled X-ray and UV flux measurements of 1598
quasars (QSOs) in the redshift range $0.036 \leq z \leq 5.1003$, part of which,
$z \sim 2.4 - 5.1$, is largely cosmologically unprobed. In this paper we use
these QSO measurements, alone and in conjunction with baryon acoustic
oscillation (BAO) and Hubble parameter [$H(z)$] measurements, to constrain
cosmological parameters in six different cosmological models, each with two
different Hubble constant priors. In most of these models, given the larger
uncertainties, the QSO cosmological parameter constraints are mostly consistent
with those from the $H(z)$ + BAO data. A somewhat significant exception is the
non-relativistic matter density parameter $\Omega_{m0}$ where the QSO data
favors $\Omega_{m0} \sim 0.5 - 0.6$ in most models. Consequently in joint
analyses of QSO data with $H(z)$ + BAO data the one-dimensional $\Omega_{m0}$
distributions shift slightly toward larger values. A joint analysis of the QSO
+ $H(z)$ + BAO data is consistent with the current standard model,
spatially-flat $\Lambda$CDM, but mildly favors closed spatial hypersurfaces and
dynamical dark energy. Since the higher $\Omega_{m0}$ values favored by the QSO
data appear to be associated with the $z \sim 2 - 5$ part of these data, and
conflict somewhat with strong indications for $\Omega_{m0} \sim 0.3$ from most
$z < 2.5$ data as well as from the cosmic microwave background anisotropy data
at $z \sim 1100$, in most models, the larger QSO data $\Omega_{m0}$ is possibly
more indicative of an issue with the $z \sim 2 - 5$ QSO data than of an
inadequacy of the standard flat $\Lambda$CDM model.
