Existence Conditions for Symmetric Generalized Vector Quasi-variational Inclusion Problems

In this paper, we establish an existence theorem by using Kakutani-Fan-Glicksberg fixed-point theorem for symmetric generalized quasi-variational inclusion problem in real locally convex Hausdorff topological vector spaces. Moreover, the closedness of the solution set for this problem is obtained. As special cases, we also derive the existence results for symmetric weak and strong quasi-equilibrium problems. The results presented in the paper improve and extend the main results in the literature.