Abstract
In this paper we give several existence results for solutions of equilibrium problems in topological spaces without linear structure. To this end we introduce a new concept of convexity for maps and multivalued maps in spaces without linear structure. The discussion on convexity is enriched with some example useful to compare the new conditions with the existing one in literature. Finally, we apply the existence results obtained to a Nash equilibrium problem and to a maximization of a binary relation.
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Acknowledgements
The first author is a member of the national research group “Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA)” of INDAM.
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Open access funding provided by Università degli Studi di Perugia within the CRUI-CARE Agreement. This research was carried out within the national group GNAMPA of INDAM. The first author is partially supported by the Department of Mathematics and Computer Science of the University of Perugia (Italy) and by the projects “Fondi di funzionamento per la ricerca dipartimentale -Anno 2021”,“Metodi della Teoria dell’Approssimazione, Analisi Reale, Analisi Nonlineare e loro applicazioni” and “Integrazione, Approssimazione, Analisi Nonlineare e loro Applicazioni”, funded by the 2018 and 2019 basic research fund of the University of Perugia.
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Benedetti, I., Martellotti, A. Set Valued Equilibrium Problems Without Linear Structure. Set-Valued Var. Anal 32, 9 (2024). https://doi.org/10.1007/s11228-024-00710-w
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DOI: https://doi.org/10.1007/s11228-024-00710-w