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 |
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ASJC Scopus subject areas
- Mathematics(all)
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On D-KKM theorem and its applications. / Pathak, H. K.; Khan, M. S.
In: Bulletin of the Australian Mathematical Society, Vol. 67, No. 1, 02.2003, p. 67-77.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On D-KKM theorem and its applications
AU - Pathak, H. K.
AU - Khan, M. S.
PY - 2003/2
Y1 - 2003/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0037307335&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037307335&partnerID=8YFLogxK
M3 - Article
VL - 67
SP - 67
EP - 77
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
SN - 0004-9727
IS - 1
ER -