  Superconductors derived from topological insulators and topological
crystalline insulators by doping have long been considered to be candidates as
topological superconductors. Pb$_{0.5}$Sn$_{0.5}$Te is a topological
crystalline insulator with mirror symmetry protected surface states on (001),
(011) and (111) oriented surfaces. The superconductor
(Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te is induced by In doping in
Pb$_{0.5}$Sn$_{0.5}$Te, and is thought to be a topological superconductor. Here
we report the first scanning tunneling spectroscopy measurement of the
superconducting state as well as the superconducting energy gap in
(Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te on a (001)-oriented surface. The
spectrum can be well fitted by an anisotropic $s$-wave gap function of
$\Delta=0.72+0.18\cos4\theta$ meV using Dynes model. The results show that the
quasi-particle density of states seem to be fully gapped without any in-gap
states, in contradiction with the expectation of a topological superconductor.
