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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.

References [Enhancements On Off] (What's this?)

  • 1. R.P. Agarwal, M. Frigon and D. O'Regan, A survey of recent fixed point theory in Fréchet spaces, Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday, Vol 1, 75-88, Kluwer Acad. Publ., Dordrecht, 2003. MR 2060212
  • 2. K. Deimling, Multivalued differential equations, Walter de Gruyter, Berlin, 1992. MR 1189795 (94b:34026)
  • 3. M. Frigon, Fixed point results for compact maps on closed subsets of Fréchet spaces and applications to differential and integral equations, Bull. Soc. Math. Belgique, 9(2002), 23-37. MR 1905646 (2003b:47089)
  • 4. L.V. Kantorovich and G.P. Akilov, Functional analysis in normed spaces, Pergamon Press, Oxford, 1964. MR 0664597 (83h:46002)
  • 5. D. O'Regan, A continuation theory for weakly inward maps, Glasgow Math. J., 40(1998), 311-321. MR 1660097 (99i:47107)
  • 6. D. O'Regan, Homotopy and Leray-Schauder type results for admissible inward multimaps, Jour. Concrete Appl. Math., 2(2004), 67-76. MR 2132353 (2005k:47123)
  • 7. S. Reich, A fixed point theorem for Fréchet spaces, Jour. Math. Anal. Appl., 78(1980), 33-35. MR 0595760 (82h:47055)

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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

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

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