Displaying similar documents to “New versions on Nikaidô's coincidence theorem”

Equilibria and strict equilibria of multivalued maps on noninvariant sets

Pierre Cardaliaguet, Grzegorz Gabor, Marc Quincampoix (2003)

Annales Polonici Mathematici

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This paper is concerned with existence of equilibrium of a set-valued map in a given compact subset of a finite-dimensional space. Previously known conditions ensuring existence of equilibrium imply that the set is either invariant or viable for the differential inclusion generated by the set-valued map. We obtain some equilibrium existence results with conditions which imply neither invariance nor viability of the given set. The problem of existence of strict equilibria is also discussed. ...

Fixed points of multivalued contractions with nonclosed, nonconvex values

Salvatore A. Marano (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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For a class of multivalued contractions with nonclosed, nonconvex values, the set of all fixed points is proved to be nonempty and arcwise connected. Two applications are then developed. In particular, one of them is concerned with some properties of the set of all classical trajectories corresponding to continuous controls for a given nonlinear control system.