Solvability of variational inequalities on Hilbert lattices

Hiroki Nishimura, Efe A. Ok

    Research output: Contribution to journalArticlepeer-review


    This paper 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.

    Original languageEnglish (US)
    Pages (from-to)608-625
    Number of pages18
    JournalMathematics of Operations Research
    Issue number4
    StatePublished - Nov 2012


    • Fixed point theorems
    • Hilbert lattices
    • Variational inequalities

    ASJC Scopus subject areas

    • General Mathematics
    • Computer Science Applications
    • Management Science and Operations Research


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