Finite-dimensional quasi-variational inequalities associated with discontinuous functions

  • P. Cubiotti
Technical Note


In this paper, given a nonempty closed convex setX n , a functionf: X→ℝ n , and a multifunction Γ:X→2X, we deal with the problem of finding a point\(\hat x\)X such that
$$\hat x \in \Gamma (\hat x) and \langle f(\hat x), \hat x - y\rangle \leqslant 0, for all y \in \Gamma (\hat x).$$
For such problem, we establish a result where, in particular, the functionf is not assumed to be continuous. More precisely, we extend to the present setting a finite-dimensional version of a result by Ricceri on variational inequalities (Ref. 1).

Key Words

Quasi-variational inequalities multifunctions fixed points lower semicontinuity 


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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • P. Cubiotti
    • 1
  1. 1.Department of MathematicsUniversity of MessinaMessinaItaly

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