  The present paper is a natural continuation of our previous paper:
"Teleparallel Lagrange geometry and a unified field theory, Class. Quantum
Grav., 27 (2010), 045005 (29pp)" \cite{WNA}. In this paper, we apply a
linearization scheme on the field equations obtained in \cite{WNA}. Three
important results under the linearization assumption are accomplished. First,
the vertical fundamental geometric objects of the EAP-space loose their
dependence on the positional argument $x$. Secondly, our linearized theory in
the Cartan-type case coincides with the GFT in the first order of
approximation. Finally, an approximate solution of the vertical field equations
is obtained.
