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A Ky Fan minimax inequality for quasiequilibria on finite dimensional spaces
Several results concerning existence of solutions of a quasiequilibrium
problem defined on a finite dimensional space are established. The proof of the
first result is based on a Michael selection theorem for lower semicontinuous
set-valued maps which holds in finite dimensional spaces. Furthermore this
result allows one to locate the position of a solution. Sufficient conditions,
which are easier to verify, may be obtained by imposing restrictions either on
the domain or on the bifunction. These facts make it possible to yield various
existence results which reduce to the well known Ky Fan minimax inequality when
the constraint map is constant and the quasiequilibrium problem coincides with
an equilibrium problem. Lastly, a comparison with other results from the
literature is discussed
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