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Volume 1, Issue 1, 30 April 2019, Pages 77-94
Abstract. In this paper, we consider optimization problems of set valued mappings on ordered sets. It leads us to define or to construct some ordering relations on the power sets of ordered sets, which play the standards for ordering different sets. On the power sets of preordered sets, we introduce three preordering relations based on the given preorder relations. Several properties of these three preordering relations are provided. Under these preordering relations, we prove some order- clustered fixed point theorems, which are applied to prove existence theorems of extended Nash equilibriums for set-valued mappings.
How to Cite this Article.
Jinlu Li, Christiane Tammer, Set optimization problems on ordered sets, Appl. Set-Valued Anal. Optim. 1 (2019), 77-94.