  Here, a non-linear analysis method is applied rather than classical one to
study projective Finsler geometry. More intuitively, by means of an inequality
on Ricci-Finsler curvature, a projectively invariant pseudo-distance is
introduced and an analogous of Schwarz' lemma in Finsler geometry is proved.
Next, the Schwarz' lemma is applied to show that the introduced pseudo-distance
is a distance. This projectively invariant distance will be served in
continuation of this work to investigate Einstein-Finsler spaces and classify
Finsler spaces as well.
