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Summary: J. Math. Anal. Appl. 296 (2004) 455472
www.elsevier.com/locate/jmaa
Collective fixed points and maximal elements
with applications to abstract economies
Lai-Jiu Lin a,
, Qamrul Hasan Ansari b,1
a Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, 50058
b Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals,
P.O. Box 1169, Dhahran 31261, Saudi Arabia
Received 4 June 2003
Available online 2 July 2004
Submitted by C.E. Chidume
Abstract
In this paper, we first establish collective fixed points theorems for a family of multivalued maps
with or without assuming that the product of these multivalued maps is -condensing. As an ap-
plication of our collective fixed points theorem, we derive the coincidence theorem for two families
of multivalued maps defined on product spaces. Then we give some existence results for maximal
elements for a family of LS-majorized multivalued maps whose product is -condensing. We also
prove some existence results for maximal elements for a family of multivalued maps which are not
LS-majorized but their product is -condensing. As applications of our results, some existence re-
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