In this article, we study a generalized variational inequality problem with multi-valued mappings over product sets and the system of generalized variational inequalities with multi-valued mappings which are equivalent problems. By developing the idea of generalized densely relatively pseudomonotone mappings, and by using well-known Fan-KKM theorem and fixed point theorem, we prove existence results of our problem. We construct an example of generalized Nash equilibrium problem in the context of our problem, and as an application of our results, we establish an existence of coincident point result.
Dense-segment set Variational inequality problem System of variational inequalities Generalized densely relatively pseudomonotone
Mathematics Subject Classification
49J40 47J20 47H10
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