  In this article, we present several inequalities treating operator means and
the Cauchy-Schwarz inequality. In particular, we present some new comparisons
between operator Heron and Heinz means, several generalizations of the
difference version of the Heinz means and further refinements of the
Cauchy-Schwarz inequality. The techniques used to accomplish these results
include convexity and L\"{o}wner matrices.
