A Ky Fan minimax inequality for quasiequilibria on finite-dimensional spaces. (English) Zbl 07032740

Summary: 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.


47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J35 Existence of solutions for minimax problems
49J40 Variational inequalities
90C30 Nonlinear programming
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