  We refine Epstein's method to prove joint concavity/convexity of matrix trace
functions of the extended Lieb type
$Tr{\Phi(A^p)^{1/2}\Psi(B^q)\Phi(A^p)^{1/2}}^s$, where $\Phi$ and $\Psi$ are
positive linear maps. By the same method combined with majorization technique,
similar properties are proved for symmetric (anti-) norm functions of the form
$||{\Phi(A^p)\sigma\Psi(B^q)}^s||$ involving an operator mean $\sigma$. Carlen
and Lieb's variational method is also used to improve the convexity property of
norm functions $||\Phi(A^p)^s||$.
