  The existence of quasi-bi-Hamiltonian structures for a two-dimensional
superintegrable $(k_1,k_2,k_3)$-dependent Kepler-related problem is studied. We
make use of an approach that is related with the existence of some complex
functions which satisfy interesting Poisson bracket relations and that was
previously applied to the standard Kepler problem as well as to some particular
superintegrable systems as the Smorodinsky-Winternitz (SW) system, the
Tremblay-Turbiner-Winternitz (TTW) and Post-Winternitz (PW) systems. We prove
that these complex functions are important for two reasons: first, they
determine the integrals of motion, and second they determine the existence of
some geometric structures (in this particular case, quasi-bi-Hamiltonian
structures).
  All the results depend of three parameters ($k_1, k_2, k_3$) in such a way
that in the particular case $k_1\ne 0$, $k_2= k_3= 0$, we recover the results
of the original Kepler problem (previously studied in SIGMA 12, 010 (2016)).
This paper can be considered as divided in two parts and every part present a
different approach (different complex functions and different
quasi-bi-Hamiltonian structures).
