A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces

Marco Castellani, Massimiliano Giuli and Massimo Pappalardo ()
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Marco Castellani: Computer Science and Mathematics
Massimiliano Giuli: Computer Science and Mathematics
Massimo Pappalardo: University of Pisa

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 1, No 3, 53-64

Abstract: Abstract 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.

Keywords: Quasiequilibrium problem; Ky Fan minimax inequality; Set-valued map; Fixed point; 47J20; 49J35; 49J40; 90C30 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10957-018-1319-0

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