On D-KKM theorem and its applications

H. K. Pathak, M. S. Khan

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)67-77
Number of pages11
JournalBulletin of the Australian Mathematical Society
Volume67
Issue number1
Publication statusPublished - Feb 2003

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KKM Theorem
Set-valued Mapping
KKM Mapping
Generalized Variational Inequality
Maximal Element
Existence Results
Theorem
Class
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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 journalArticle

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