On D-KKM theorem and its applications

H. K. Pathak; M. S. Khan

On D-KKM theorem and its applications

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

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

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 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

ASJC Scopus subject areas

Mathematics(all)

Cite this

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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.

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On D-KKM theorem and its applications

Abstract

ASJC Scopus subject areas

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