  We establish conditions for the discrete versions of logarithmic concavity
and convexity of the higher order regularized basic hypergeometric function
with respect simultaneous shift of all its parameters. For a particular case of
Heine's basic hypergeometric function we prove logarithmic concavity and
convexity with respect to the bottom parameter. We further establish a
linearization identity for the generalized Tur\'{a}nian formed by a particular
case of Heine's basic hypergeometric function. Its $q=1$ case also appears to
be new.
