Order preservation of solution correspondence to single-parameter generalized variational inequalities on Hilbert lattices

We establish order preservation of solution correspondence provided that the set-valued mapping has bounded order-closed values for each parameter of single-parameter generalized variational inequalities on Hilbert lattices. This work is different from the earlier results which assume that set-valued mapping has compact values. An example is used to show their difference. We also investigate order preservation of solution correspondence on the Tikhonov Regularization method for generalized variational inequality problem. In addition, more details about the connection between the structure of norm and order in Hilbert lattices are listed.