Levitin-Polyak well-posedness for lexicographic vector equilibrium problems

We introduce the notions of Levitin-Poljak (LP) well-posedness and LP well-posedness in the generalized sense for the lexicographic vector equilibrium problems. Then, we establish some sufficient conditions for lexicographic vector equilibrium problems to be LP well-posedness at the reference point. Numerous examples are provided to explain that all the assumptions we impose are very relaxed and cannot be dropped. The results in this paper unify, generalize and extend some known results in the literature.