  The Newton-Raphson basins of attraction, associated with the libration points
(attractors), are revealed in the pseudo-Newtonian planar circular restricted
three-body problem, where the primaries have equal masses. The parametric
variation of the position as well as of the stability of the equilibrium points
is determined, when the value of the transition parameter $\epsilon$ varies in
the interval $[0,1]$. The multivariate Newton-Raphson iterative scheme is used
to determine the attracting domains on several types of two-dimensional planes.
A systematic and thorough numerical investigation is performed in order to
demonstrate the influence of the transition parameter on the geometry of the
basins of convergence. The correlations between the basins of attraction and
the corresponding required number of iterations are also illustrated and
discussed. Our numerical analysis strongly indicates that the evolution of the
attracting regions in this dynamical system is an extremely complicated yet
very interesting issue.
