  We make use of a result of Hurwitz and Reznick, and a consequence of this
result due to Fidalgo and Kovacec, to determine a new sufficient condition for
a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of
squares. This result generalizes a result of Lasserre and a result of Fidalgo
and Kovacec, and it also generalizes the improvements of these results given in
[6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we
explain how $f_{gp}$ can be computed using geometric programming. The lower
bound $f_{gp}$ is generally not as good as the lower bound $f_{sos}$ introduced
by Lasserre and Parrilo and Sturmfels, which is computed using semidefinite
programming, but a run time comparison shows that, in practice, the computation
of $f_{gp}$ is much faster. The computation is simplest when the highest degree
term of $f$ has the form $\sum_{i=1}^n a_iX_i^{2d}$, $a_i>0$, $i=1,...,n$. The
lower bounds for $f$ established in [6] are obtained by evaluating the
objective function of the geometric program at the appropriate feasible points.
