Set Valued Equilibrium Problems Without Linear Structure-Reference-Cited by-同舟云学术

Set Valued Equilibrium Problems Without Linear Structure

Published:2024-03-18 Issue:2 Volume:32 Page:
ISSN:1877-0533
Container-title:Set-Valued and Variational Analysis
language:en
Short-container-title:Set-Valued Var. Anal

Author:

Benedetti Irene^ORCID,Martellotti Anna

Abstract

AbstractIn 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.

Funder

Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

University of Perugia

Università degli Studi di Perugia

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s11228-024-00710-w.pdf

Reference38 articles.

1. Alleche, B., Radulescu, V.D.: Further on set-valued equilibrium problems and applications to Browder variational inclusions. J. Optim. Theory Appl. 175, 39–58 (2017)

2. Alleche, B., Radulescu, V.D.: Further on set-valued equilibrium problems in the pseudo-monotone case and applications to Browder variational inclusions. Optim. Lett. 12, 1789–1810 (2018)

3. Bardaro, C., Ceppitelli, R.: Fixed point theorems and vector-valued minimax theorems. J. Math. Anal. Appl. 146, 369–373 (1990)

4. Bardaro, C., Ceppitelli, R.: Some generalizations in H-modular spaces of Fan’s best approximation theorem. J. Aust. Math. Soc. 56, 291–302 (1994)

5. Baye, M.R., Tian, G., Zhou, J.: Characterizations of the existence of equilibria in games with discontinuous and non-quasiconcave payoffs. Rev. Econ. Stud. 60, 935–948 (1993)