Existence conditions for symmetric generalized quasi-variational inclusion problems

Abstract

In this paper, we establish an existence theorem by using the Kakutani-Fan-Glicksberg fixed-point theorem for a 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. MSC: 90B20; 49J40

Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces

“…Using the properties of graph convergence of (H, ϕ)-η-monotone operator, we construct a new class of iterative algorithms to solve the system of generalized variational-like inclusions involving (H, ϕ)-η-monotone operator in semi-inner product spaces. Using the technique in this paper, one may generalize the results for symmetric generalized quasi-variational inclusion problems considered in [1,11]. The methods and results presented in this paper improve and generalize many known results in the literature.…”

On a generalized variational inequality problem

“…Similar conditions like in Theorem 2.1 could be used to obtain existence results for some other variational problems, for instance for problems of the sort treated in [2], [12][13][14], [16].…”