  The masses and radii of strongly magnetized anisotropic deformed white dwarf
stars are investigated using the stellar structure equations in the
parameterized $\gamma$-metric formalism. The Equation of State (EoS) of a
completely degenerate relativistic electron gas in strong quantizing
density-dependent magnetic field is developed. The fluid and field pressure
anisotropy among the parallel and perpendicular components to the magnetic
field is taken into consideration. This anisotropy in the EoS causes
axisymmetric deformation of the star. We found stable solutions of deformed
super-Chandrasekhar ultramassive white dwarfs. The masses of anisotropic
magnetized white dwarfs at the same central density decrease monotonically with
the increase in the strength of the central magnetic field, while the
equatorial radii increase monotonically. This is in sharp contrast to the
isotropic case where both the mass and radius increase monotonically. High
magnetic field increases anisotropy and oblateness. We also see that the
maximum mass and its corresponding equatorial radius both decrease as central
magnetic field strength increases. We also notice that the maximum mass occurs
at higher central density as the magnetic field increases. This shows that
increasing magnetic field (hence increasing anisotropy) softens the EoS and
makes the star more compact.
