Fixed-point theory of one-dimensional maps of ℝ
does
not completely address the issue of nonhyperbolic fixed points.
This note generalizes the existing tests to completely classify
all such fixed points. To do this, a family of operators are
exhibited that are analogous to generalizations of the Schwarzian
derivative. In addition, a family of functions f are exhibited
such that the Maclaurin series of f(f(x)) and x are identical.