Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological fixed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the involved (set-valued) maps be hemicontinuous or monotonic. Some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work, and appear to have scope for applications. This is illustrated by means of several applications to fixed point theory, optimization, and game theory.
['Hiroki Nishimura', 'Efe A. Ok']
I am writing a research paper on a idea Solvability of Variational Inequalities on Hilbert Lattices
[{"from": "human", "value": "I am writing a research paper on a idea Solvability of Variational Inequalities on Hilbert Lattices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological fixed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the involved (set-valued) maps be hemicontinuous or monotonic. Some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work, and appear to have scope for applications. This is illustrated by means of several applications to fixed point theory, optimization, and game theory."}]