  An important problem in analysis on fractals is the existence of a
self-similar energy on finitely ramified fractals. The self-similar energies
are constructed in terms of eigenforms, that is, eigenvectors of a special
nonlinear operator. Previous results by C. Sabot and V. Metz give conditions
for the existence of an eigenform. In this paper, I give a different and
probably shorter proof of the previous results, which appears to be suitable
for improvements. Such a proof is based on a fixed-point theorem for
anti-attracting maps on a convex set.
