We propose a model for the vector-like lepton to explain small muon mass by seesaw mechanism, based on lepton-specific two Higgs doublet models with local $$U(1)'$$ symmetry. There is no bare nonzero charge of leptophilic doublet, so physical generated due mixing between and after dark get VEVs. In this scenario, non-decoupling effects give rise leading contributions $$g-2$$ , thanks light $$Z'...

In this paper, we consider the system of vector quasi-equilibrium problems with or without involving -condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibr...