EXISTENCE CONDITIONS FOR SET-VALUED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON HADAMARD MANIFOLDS WITH VARIABLE DOMINATION STRUCTURE AND APPLICATIONS

In this paper, set-valued strong vector quasi-equilibrium problems and set-valued weak vector quasi-equilibrium problems with variable domination structure (for short, (SSVQEPM) and (SWVQEPM), respectively) are considered in the setting of Hadamard manifolds. Then we establish some existence results for solutions of these problems by using the Kakutani-Fan-Glicksberg type fixed point theorem in the setting of Hadamard manifolds. Moreover, some applications to generalized strong (resp. weak) vector quasi-variational-like inequalities and generalized vector optimization problems are also presented on Hadamard manifolds. Some examples are given for the illustration of our results.