  We present the Fokker-Planck equation (FPE) for an inhomogeneous medium with
a position-dependent mass particle by making use of the Langevin equation, in
the context of a generalized deformed derivative for an arbitrary deformation
space where the linear (nonlinear) character of the FPE is associated with the
employed deformed linear (nonlinear) derivative. The FPE for an inhomogeneous
medium with a position-dependent diffusion coefficient is equivalent to a
deformed FPE within a deformed space, described by generalized derivatives, and
constant diffusion coefficient. The deformed FPE is consistent with the
diffusion equation for inhomogeneous media when the temperature and the
mobility have the same position-dependent functional form as well as with the
nonlinear Langevin approach. The deformed version of the H-theorem permits to
express the Boltzmann-Gibbs entropic functional as a sum of two contributions,
one from the particles and the other from the inhomogeneous medium. The
formalism is illustrated with the infinite square well and the confining
potential with linear drift coefficient. Connections between superstatistics
and position-dependent Langevin equations are also discussed.
