Generalized KKM theorems on hyperconvex metric spaces and some applications
β Scribed by Tong-Huei Chang; Chi-Ming Chen; Chin-Yueh Peng
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 207 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this work, we establish the intersection property for a family of admissible subsets in a hyperconvex metric space, and we apply this intersection property to get generalized KKM theorems, coincidence theorems, variational inequality theorems and minimax inequality theorems.
π SIMILAR VOLUMES
In hyperconvex metric spaces, we introduce KnasterαKuratowskiαMazurkiewicz mappings. Then we prove an analogue to Ky Fan's fixed point theorem in hyperconvex metric spaces.
Some new generalized G-KKM and generalized S-KKM theorems are proved under the noncompact setting of generalized convex spaces. As applications, some new minimax inequalities, saddle point theorems, a coincidence theorem, and a fixed point theorem are given in generalized convex spaces. These theore