|
Fixed points of compact Kakutani maps with antipodal boundary conditions
Author(s):
Donal
O'Regan;
Juan
Perán
Journal:
Proc. Amer. Math. Soc.
134
(2006),
825-830.
MSC (2000):
Primary 47H10, 54H25
Posted:
September 20, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove a fixed-point result for compact upper semicontinuous compact-convex-valued multifunctions satisfying antipodal boundary conditions on bounded symmetric subsets of a normed space. Two types or antipodal conditions are considered.
References:
-
- 1.
- R. P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge Universty Press, Cambridge, 2001. MR 1825411 (2002c:47122)
- 2.
- G. Beer, Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers, Dordrecht, 1993. MR 1269778 (95k:49001)
- 3.
- A. Cellina, A Theorem on the approximation of compact multi-valued mappings, Atti Accad. Naz. Lincei Cl. Sci. Fis., Mat. Natur. Rend. (8) 47 (1969), 429-433. MR 0276936 (43:2676)
- 4.
- S. Y. Chang, Borsuk's antipodal and fixed-point theorems for set-valued maps, Proc. Amer. Math. Soc. 121 (1994) no. 3, 937-941. MR 1221720 (94i:55003)
- 5.
- L. Górniewicz, Topological fixed point theory of multivalued mappings, Mathematics and its Applications, No. 495, Kluwer Academic Publishers, Dordrecht, 1999. MR 1748378 (2001h:58010)
- 6.
- A. Granas, Theorem on antipodes and theorems on fixed points for a certain class of multi-valued mappings in Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 No. 5 (1959), 271-275. MR 0117588 (22:8365)
- 7.
- A. Granas and J. Dugundji, Fixed point theory, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. MR 1987179 (2004d:58012)
- 8.
- T.W. Ma, Topological degrees of set-valued compact fields in locally convex spaces, Dissertationes Math. Rozprawy Mat. 92 (1972). MR 0309103 (46:8214)
- 9.
- L. Nirenberg, Topics in nonlinear functional analysis, New York Univ. Lecture Notes, New York, 1974.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
47H10, 54H25
Retrieve articles in all Journals with MSC
(2000):
47H10, 54H25
Additional Information:
Donal
O'Regan
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland
Juan
Perán
Affiliation:
Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Apartado 60149, Madrid, 28080, Spain
Email:
jperan@ind.uned.es
DOI:
10.1090/S0002-9939-05-08179-7
PII:
S 0002-9939(05)08179-7
Received by editor(s):
October 20, 2004
Posted:
September 20, 2005
Additional Notes:
This research was supported in part by Ministerio de Ciencia y Tecnología (Spain), project MTM2004-06652-C03-03.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2005,
American Mathematical Society
|
Comments: webmaster@ams.org