  We present several matrix and operator inequalities of Hermite-Hadamard type.
We first establish a majorization version for monotone convex functions on
matrices. We then utilize the Mond-Pecaric method to get an operator version
for convex functions. We also present some applications. Finally we obtain an
Hermite-Hadamard inequality for operator convex functions, positive linear maps
and operators acting on Hilbert spaces.
