@article{Xia2025, 
author = {Shunyou Xia and Chongyi Zhong and Chunrong Mo},
title = {A common fixed point theorem and its applications in abstract convex spaces},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {5236-5245},
keywords = {H0-condition, abstract convex space, the family of generalized equi-KKM mappings, common fixed points, generalized abstract equilibrium problems},
url = {https://www.sciopen.com/article/10.3934/math.2025240},
doi = {10.3934/math.2025240},
abstract = {First, this paper introduces a family of generalized equi-KKM mappings and the concept of quasi-abstract convexity (concavity) defined by parameter multi-valued mappings in abstract convex spaces that satisfy the        H    0  -condition. Then, using the Brouwer fixed-point theorem, we prove a common fixed-point theorem for this family of generalized equi-KKM mappings. Finally, we introduce two classes of generalized abstract equilibrium problems and obtain two existence theorems for their solutions, as an application of the common fixed-point theorem.}
}