  We present some reverse Young-type inequalities for the Hilbert-Schmidt norm
as well as any unitarily invariant norm. Furthermore, we give some inequalities
dealing with operator means. More precisely, we show that if $A, B\in
{\mathfrak B}(\mathcal{H})$ are positive operators and $r\geq 0$,
$A\nabla_{-r}B+2r(A\nabla B-A\sharp B)\leq A\sharp_{-r}B$ and prove that
equality holds if and only if $A=B$. We also establish several reverse
Young-type inequalities involving trace, determinant and singular values. In
particular, we show that if $A, B$ are positive definite matrices and $r\geq
0$, then $\label{reverse_trace} \mathrm{tr}((1+r)A-rB)\leq
\mathrm{tr}|A^{1+r}B^{-r} |-r(\sqrt{\mathrm{tr} A} - \sqrt{\mathrm{tr}
B})^{2}$.
