Lower semicontinuity of solution mappings for parametric fixed point   problems with applications
  In this paper, we establish the lower semicontinuity of the solution mapping and of the approximate solution mapping for parametric fixed point problems under some suitable conditions. As applications, the lower semicontinuity result applies to the parametric vector quasi-equilibrium problem, and allows to prove the existence of solutions for generalized Stackelberg games. 
Yu Han and Nan-jing Huang
math.OC