EXISTENCE OF SOLUTIONS TO SET-VALUED QUASI-VARIATIONAL INCLUSION PROBLEMS ON HADAMARD MANIFOLDS AND APPLICATIONS

摘要

In this paper, first we introduce two classes of set-valued quasi-variational inclusion problems and the notion of set-valued mapping being geodesic R-quasiconvexity-like in the setting of Hadamard manifolds. Then, we establish some conditions for the existence of solutions for such problems by using a Browder-type fixed point theorem in the noncompact setting on Hadamard manifolds. Finally, as applications, we consider the special cases of set-valued vector quasi-equilibrium problems, generalized vector quasi-variational-like inequalities and generalized vector quasi-optimization problems on Hadamard manifolds. Using the general framework of geodesic R-quasiconvexity-likeness and the broad problem class of quasi-variational inclusion problems, allows us to reestablish and improve corresponding existence results from the recent literature for these example applications. Some simple examples are given for the illustration of our results.