We study the relationship between the multiplicity of a fixed point of a
function g, and the dependence on epsilon of the length of epsilon-neighborhood
of any orbit of g, tending to the fixed point. The relationship between these
two notions was discovered before by Elezovic, Zubrinic, Zupanovic in the
differentiable case, and related to the box dimension of the orbit. Here, we
generalize these results to non-differentiable cases. We study the space of
functions having a development in a Chebyshev scale and use multiplicity with
respect to this space of functions.