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Fixed point theory for weakly inward Kakutani maps: The projective limit approach
Author(s):
Ravi
P.
Agarwal;
Donal
O'Regan
Journal:
Proc. Amer. Math. Soc.
135
(2007),
417-426.
MSC (2000):
Primary 47H10
Posted:
August 4, 2006
MathSciNet review:
2255288
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Additional information
Abstract:
New fixed point results are presented for weakly inward Kakutani condensing maps defined on a Fréchet space  . The proofs rely on the notion of an essential map and viewing  as the projective limit of a sequence of Banach spaces.
References:
-
- 1.
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- 2.
- K. Deimling, Multivalued differential equations, Walter de Gruyter, Berlin, 1992. MR 1189795 (94b:34026)
- 3.
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- 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)
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- 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)
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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:
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
Posted:
August 4, 2006
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2006,
American Mathematical Society
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