### 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 |
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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.