### 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 sign_{C}(X, Y), double-struct V sign_{C} (X, Y), double-struct A sign_{C}(X, Y) and U-fraktur sign_{C}(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)

### Cite this

*Bulletin of the Australian Mathematical Society*,

*67*(1), 67-77.

**On D-KKM theorem and its applications.** / Pathak, H. K.; Khan, M. S.

Research output: Contribution to journal › Article

*Bulletin of the Australian Mathematical Society*, vol. 67, no. 1, pp. 67-77.

}

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

AN - SCOPUS:0037307335

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 -