Some Existence Results for a Class of Relatively B-pseudomonotone Variational Inequalities over Product Sets

The problems which imply variational inequality over product sets have many applications. Thus, the Nash equilibrium problem for differentiable functions, various equilibrium-type problems, as traffic equilibrium, spatial equilibrium and general equilibrium programming problems from economics, game theory, operations research, mathematical physics, for example, can be modelled as variational inequality problems [4, 10, 13, 14, 8, 12, 15]. For new results relative to this field see, for example, Pang [15], Konnov [9], Ansari and Yao [1,2], Yang and Yao [18], Ansari and Khan [3]. Thus in [3], without using arguments from generalized monotonicity, a concept of relatively B-pseudomonotonicity in the sense of Brezis [5,6] is introduced. In this paper, we consider a general class of variational inequalities over product sets, which extend many known results in this field. Then, using a fixed point theorem of Chowdhury and Tan [7], some existence results on the solution of problems in our class are derived.