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

A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces J Optim Theory Appl https://doi.org/10.1007/s10957-018-1319-0 A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces 1 1 Marco Castellani · Massimiliano Giuli · Massimo Pappalardo Received: 5 December 2017 / Accepted: 19 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 quasiequilib- rium 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 Mathematics Subject Classification 47J20 · 49J35 · 49J40 · 90C30 1 Introduction In [1] the author established the famous Ky Fan http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
D.O.I.
10.1007/s10957-018-1319-0
Publisher site
See Article on Publisher Site

Abstract

J Optim Theory Appl https://doi.org/10.1007/s10957-018-1319-0 A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces 1 1 Marco Castellani · Massimiliano Giuli · Massimo Pappalardo Received: 5 December 2017 / Accepted: 19 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 quasiequilib- rium 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 Mathematics Subject Classification 47J20 · 49J35 · 49J40 · 90C30 1 Introduction In [1] the author established the famous Ky Fan

Journal

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Jun 4, 2018

References

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