Characterizations of $L$-concavities and $L$-convexities via derived relations

Authors : Xiuyun WU, Erqiang Lİ

Pages : 876-895

Doi:10.15672/hujms.1175332

View : 163 | Download : 186

Publication Date : 2023-08-15

Article Type : Research Paper

Abstract :This paper is to characterize $L$-concavities and $L$-convexities via some derived forms of relations and operators. Specifically, notions of $L$-concave derived internal relation space and $L$-concave derived hull space are introduced. It is proved that the category of $L$-concave derived internal relation spaces and the category of $L$-concave derived hull spaces are isomorphic to the category of $L$-concave spaces. Also, notions of $L$-convex derived enclosed relation space and $L$-convex derived hull space are introduced. It is proved that the category of $L$-convex derived enclosed relation spaces and the category of $L$-convex derived hull spaces are isomorphic to the category of $L$-convex spaces.
Keywords : L concave derived internal relation space, L convex derived enclosed relation space, L concave derived hull space, L convex derived hull space