  In this paper, we investigate the change of Finslr metrics $$L(x,y)
\to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a
generalized $\beta$-conformal change. Under this change, we study some special
Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible,
$C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the
transformation of the T-tensor under this change and study some interesting
special cases. We then impose a certain condition on the generalized
$\beta$-conformal change, which we call the b-condition, and investigate the
geometric consequences of such condition. Finally, we give the conditions under
which a generalized $\beta$-conformal change is projective and generalize some
known results in the literature.
