@article{Gao2026, 
author = {Ruimin Gao and Chaoli Yao},
title = {Abstract convex theory for set-valued sub-topical mappings},
year = {2026},
journal = {Natural Science of Hainan University},
volume = {44},
number = {4},
pages = {430-439},
keywords = {set-valued sub-topical mapping, abstract convex analysis, partially ordered supremum, set-valued support},
url = {https://www.sciopen.com/article/10.65658/j.hndk.2026011902},
doi = {10.65658/j.hndk.2026011902},
abstract = {Sub-topical functions constitute a significant class of abstract convex functions and play a pivotal role in optimization theory. However, the scalar framework of sub-topical functions faces limitations when addressing set-valued optimization problems equipped with order structures. To bridge this gap, this paper generalizes the concept of sub-topicality from scalar-valued mappings to set-valued mappings. By leveraging the notion of weak supremum in vector spaces, we first construct a class of set-valued elementary mappings with specific algebraic properties to serve as supporting elements. Subsequently, we introduce the support set for these set-valued sub-topical mappings and establish their upper envelope representation with respect to this family of elementary mappings. Finally, we develop a comprehensive abstract convexity theory for set-valued sub-topical mappings. This framework lays a solid theoretical foundation for future research in set-valued optimization and related fields.}
}