  The purpose of this paper is to extend the recent work of Paul &
Bandyopadhyay [Astrophys. Space Sci. 361, 172(2016)] on the existence of
different dust ion acoustic solitary structures in an unmagnetized
collisionless dusty plasma consisting of negatively charged static dust grains,
adiabatic warm ions, nonthermal electrons and isothermal positrons in a more
generalized form by considering nonthermal positrons instead of isothermal
positrons. The present system supports both positive and negative potential
double layers, coexistence of solitary waves of both polarities and positive
potential supersolitons. The qualitative and the quantitative changes in
existence domains of different solitary structures which occur for the presence
of nonthermal positrons have been presented in comparison with the results of
Paul & Bandyopadhyay [Astrophys. Space Sci. 361, 172(2016)]. The formation of
supersoliton structures and their limitations have been analyzed with the help
of phase portraits of the dynamical system corresponding to the dust ion
acoustic solitary structures. Phase portrait analysis clearly indicates a
smooth transition between soliton and supersoliton.
