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

Year 2023, Volume: 52 Issue: 4, 876 - 895, 15.08.2023

Xiu-yun Wu , Er-qiang Li

https://doi.org/10.15672/hujms.1175332

Cited By: 1

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

Supporting Institution

Anhui Educational committee; Anhui Normal University; Henan University of Science and Technology

Project Number

KJ2020A0056; 751966; 13480055

Thanks

University Science Research Project of Anhui Province (KJ2020A0056); Doctoral Scientific Research Foundation of Anhui Normal University (751966); Doctoral Scientific Research Foundation of Henan University of Science and Technology (13480055)

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