On D-KKM theorem and its applications

H. K. Pathak*, M. S. Khan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number1
Publication statusPublished - Feb 2003

ASJC Scopus subject areas

  • General Mathematics


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