Quasi-equilibrium problems generalize equilibrium problems, as introduced in the framework of Blum and Oettli. This study focuses on quasi-equilibrium problems in which the constraint map is not a self-map. We present various reformulations that establish existence results for projected solutions in Banach spaces. Furthermore, we apply these findings to quasi-variational inequalities and quasi-optimization problems.
Bianchi, M., Cotrina, J., García, Y., Pini, R. (2025). Different approaches to the existence of projected solutions in Banach spaces. OPTIMIZATION, 1-18 [10.1080/02331934.2025.2553195].
Different approaches to the existence of projected solutions in Banach spaces
Pini R.
2025
Abstract
Quasi-equilibrium problems generalize equilibrium problems, as introduced in the framework of Blum and Oettli. This study focuses on quasi-equilibrium problems in which the constraint map is not a self-map. We present various reformulations that establish existence results for projected solutions in Banach spaces. Furthermore, we apply these findings to quasi-variational inequalities and quasi-optimization problems.
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