  The semirelativistic Hamiltonian H = \beta\sqrt{m^2 + p^2} + V(r), where V(r)
is a central potential in R^3, is concave in p^2 and convex in p. This fact
enables us to obtain complementary energy bounds for the discrete spectrum of
H. By extending the notion of 'kinetic potential' we are able to find general
energy bounds on the ground-state energy E corresponding to potentials with the
form V = sum_{i}a_{i}f^{(i)}(r). In the case of sums of powers and the log
potential, where V(r) = sum_{q\ne 0} a(q) sgn(q)r^q + a(0)ln(r), the bounds can
all be expressed in the semi-classical form E \approx \min_{r}{\beta\sqrt{m^2 +
1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}. 'Upper' and 'lower'
P-numbers are provided for q = -1,1,2, and for the log potential q = 0. Some
specific examples are discussed, to show the quality of the bounds.
