  Fe{j}\'er and Levin-Ste\v{c}kin inequalities treat integrals of the product
of convex functions with symmetric functions. The main goal of this article is
to present possible matrix versions of these inequalities. In particular,
majorization results are shown of Fej\'{e}r type for both convex and log-convex
functions. For matrix Levin-Ste\v{c}kin type, we present more rigorous results
involving the partial Loewner ordering for Hermitian matrices.
