Generalized set-valued Ekeland variational principles via the null set concept with applications to some set-valued optimization problems

Abstract

In this paper, we establish two new versions of generalized set-valued Ekeland variational principles related to the so-called null set in a hyperspace ordered by a convex cone. Moreover, we propose some interval versions of Ekeland variational principles. As applications, the obtained theoretical results are applied to prove a set-valued fixed point theorem, to solve a set-valued optimization problem, and to explore a set-valued noncooperative game.