Existence Results for Generalized Vector Quasi-Equilibrium Problems in Hadamard Manifolds

The purpose of this article was to establish manifold versions of existence theorems for generalized vector quasi-equilibrium problems in locally compact and sigma-compact spaces without any continuity assumption. The fixed-point theorem in a product Hadamard manifold is the key focus of our discussion. We further applied our theorems to saddle point and minimax problems.