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On D-KKM theorem and its applications

Published online by Cambridge University Press:  17 April 2009

H. K. Pathak  and
M. S. Khan
H. K. Pathak
Affiliation:
Department of Mathematics, Kalyan Mahavidyalaya, Bhilai Nagar (C.G.)490006, India
M. S. Khan
Affiliation:
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Al-Khod, Muscat, Sultanate of Oman
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Abstract

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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 (X, Y), C(X, Y), C (X, Y), C (X, Y) and C (X, Y). In the sequel, we apply our theorem to get some existence results for maximal elements, generalised variational inequalities, and price equilibria.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 67 - 77
Copyright
Copyright © Australian Mathematical Society 2003

References

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