  The planar equilateral restricted four-body problem where two of the
primaries have equal masses is used in order to determine the Newton-Raphson
basins of convergence associated with the equilibrium points. The parametric
variation of the position of the libration points is monitored when the value
of the mass parameter $m_3$ varies in predefined intervals. The regions on the
configuration $(x,y)$ plane occupied by the basins of attraction are revealed
using the multivariate version of the Newton-Raphson iterative scheme. The
correlations between the attracting domains of the equilibrium points and the
corresponding number of iterations needed for obtaining the desired accuracy
are also illustrated. We perform a thorough and systematic numerical
investigation by demonstrating how the dynamical parameter $m_3$ influences the
shape, the geometry and the degree of fractality of the converging regions. Our
numerical outcomes strongly indicate that the mass parameter is indeed one of
the most influential factors in this dynamical system.
