  We give a new type of mixed discrete joint universality properties, which is
satisfied by a wide class of zeta-functions. We study the universality for a
certain modification of a Matsumoto zeta-function and a periodic Hurwitz
zeta-function under certain arithmetic condition on the common difference of
arithmetical progression and the shifting parameter. Also we generalize a known
discrete universality result in our former paper and the new one as well.
