On equilibrium problems without closure of the constraint set and application to minimax problems
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In this paper, we establish sufficient conditions for the existence of solutions to the set-valued equilibrium problem without requiring the closure of the constraint set. Additionally, the conditions for the semi-continuity and convexity of the objective function are only needed on a special subset of the constraint set, rather than covering its entire domain. As applications, we derive existence results for minimax problems on dense sets.
Abstract
In this paper, we establish sufficient conditions for the existence of solutions to the set-valued equilibrium problem without requiring the closure of the constraint set. Additionally, the conditions for the semi-continuity and convexity of the objective function are only needed on a special subset of the constraint set, rather than covering its entire domain. As applications, we derive existence results for minimax problems on dense sets.