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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fixed point theory for weakly inward Kakutani maps: The projective limit approach


Authors: Ravi P. Agarwal and Donal O'Regan
Journal: Proc. Amer. Math. Soc. 135 (2007), 417-426
MSC (2000): Primary 47H10
Published electronically: August 4, 2006
MathSciNet review: 2255288
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Abstract: New fixed point results are presented for weakly inward Kakutani condensing maps defined on a Fréchet space $ E$. The proofs rely on the notion of an essential map and viewing $ \,E\,$ as the projective limit of a sequence of Banach spaces.


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Additional Information

Ravi P. Agarwal
Affiliation: Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida 32901

Donal O'Regan
Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08680-1
PII: S 0002-9939(06)08680-1
Keywords: Fixed point, weakly inward, Kakutani condensing map, essential map, projective limit.
Received by editor(s): August 29, 2005
Published electronically: August 4, 2006
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society