Abstract
In this paper, we introduce a new class of set-valued mappings in a non-convex setting called D-KKM mappings and prove a general D-KKM theorem. This extends and improves the KKM theorem for several families of set-valued mappings, such as double-struck M sign(X, Y), double-struck K signC(X, Y), double-struct V signC (X, Y), double-struct A signC(X, Y) and U-fraktur signC(X, Y). In the sequel, we apply our theorem to get some existence results for maximal elements, generalised variational inequalities, and price equilibria.
| Original language | English |
|---|---|
| Pages (from-to) | 67-77 |
| Number of pages | 11 |
| Journal | Bulletin of the Australian Mathematical Society |
| Volume | 67 |
| Issue number | 1 |
| Publication status | Published - Feb 2003 |
ASJC Scopus subject areas
- Mathematics(all)
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Cite this
Pathak, H. K., & Khan, M. S. (2003). On D-KKM theorem and its applications. Bulletin of the Australian Mathematical Society, 67(1), 67-77.