Heinz mean

The Heinz mean of two non-negative real numbers $$A$$ and $$B$$ was defined by Bhatia as:
 * $$H_x(A, B) = \frac{A^x B^{1-x} + A^{1-x} B^x}{2}$$.

with 0 &le; x &le; 1/2.

For different values of x, this Heinz mean interpolates between the arithmetic (x = 0) and geometric (x = 1/2) means such that for 0 < x < 1/2:
 * $$ \sqrt{A B} = H_{1/2}(A, B) < H_x(A, B) < H_0(A, B) = \frac{A + B}{2}$$.